{"title":"Asymptotical dynamics for non-autonomous stochastic equations driven by a non-local integro-differential operator of fractional type","authors":"Wenqiang Zhao","doi":"10.5186/AASFM.2019.4414","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4414","url":null,"abstract":"","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":"93 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78737175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
If 0 < p < ∞ and α > −1, the space of Dirichlet type D α consists of those functions f which are analytic in the unit disc D and have the property that f ′ belongs to the weighted Bergman space A α . Of special interest are the spaces Dp p−1 (0 < p < ∞) and the analytic Besov spaces B = Dp p−2 (1 < p < ∞). Let B denote the Bloch space. It is known that the closure of B (1 < p < ∞) in the Bloch norm is the little Bloch space B0. A description of the closure in the Bloch norm of the spaces H ∩B has been given recently. Such closures depend on p. In this paper we obtain a characterization of the closure in the Bloch norm of the spaces D α ∩ B (1 ≤ p < ∞, α > −1). In particular, we prove that for all p ≥ 1 the closure of the space Dp p−1 ∩ B coincides with that of H ∩ B. Hence, contrary with what happens with Hardy spaces, these closures are independent of p. We apply these results to study the membership of Blaschke products in the closure in the Bloch norm of the spaces D α ∩ B.
当0 < p <∞且α > - 1时，Dirichlet型空间D α由在单位圆盘D中解析的函数f构成，并且具有f '属于加权Bergman空间A α的性质。特别有趣的是空间Dp p−1 (0 < p <∞)和解析Besov空间B = Dp p−2 (1 < p <∞)。设B表示布洛赫空间。已知B (1 < p <∞)在Bloch范数上的闭包是小Bloch空间B0。最近给出了空间H∩B的Bloch范数中的闭包的描述。这样的闭包依赖于p。在本文中，我们得到了空间D α∩B(1≤p <∞，α > - 1)的Bloch范数中闭包的一个表征。特别地，我们证明了对于所有p≥1，空间Dp p−1∩B的闭包与H∩B的闭包重合。因此，与Hardy空间相反，这些闭包与p无关。我们应用这些结果研究了空间D α∩B的Bloch范数中闭包中的Blaschke积的隶属度。
{"title":"The closure of Dirichlet spaces in the Bloch space","authors":"P. Galanopoulos, D. Girela","doi":"10.5186/AASFM.2019.4402","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4402","url":null,"abstract":"If 0 < p < ∞ and α > −1, the space of Dirichlet type D α consists of those functions f which are analytic in the unit disc D and have the property that f ′ belongs to the weighted Bergman space A α . Of special interest are the spaces Dp p−1 (0 < p < ∞) and the analytic Besov spaces B = Dp p−2 (1 < p < ∞). Let B denote the Bloch space. It is known that the closure of B (1 < p < ∞) in the Bloch norm is the little Bloch space B0. A description of the closure in the Bloch norm of the spaces H ∩B has been given recently. Such closures depend on p. In this paper we obtain a characterization of the closure in the Bloch norm of the spaces D α ∩ B (1 ≤ p < ∞, α > −1). In particular, we prove that for all p ≥ 1 the closure of the space Dp p−1 ∩ B coincides with that of H ∩ B. Hence, contrary with what happens with Hardy spaces, these closures are independent of p. We apply these results to study the membership of Blaschke products in the closure in the Bloch norm of the spaces D α ∩ B.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":"28 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85311276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the absolutely continuous characterization of Sobolev functions on compact and connected 1-dimensional metric spaces X . We generalize the definition of absolutely continuous functions to such spaces and prove the equivalence between the absolutely continuous functions and Newtonian Sobolev functions. We also show that a compact and 1Ahlfors regular metric space X supports a p-Poincaré inequality for 1 ≤ p ≤ ∞ if and only if X is quasiconvex. As a result, the absolutely continuous functions are equivalent to the Sobolev functions defined via several different approaches.
{"title":"Absolutely continuous functions on compact and connected 1-dimensional metric spaces","authors":"Xiaodan Zhou","doi":"10.5186/AASFM.2019.4412","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4412","url":null,"abstract":"In this paper, we study the absolutely continuous characterization of Sobolev functions on compact and connected 1-dimensional metric spaces X . We generalize the definition of absolutely continuous functions to such spaces and prove the equivalence between the absolutely continuous functions and Newtonian Sobolev functions. We also show that a compact and 1Ahlfors regular metric space X supports a p-Poincaré inequality for 1 ≤ p ≤ ∞ if and only if X is quasiconvex. As a result, the absolutely continuous functions are equivalent to the Sobolev functions defined via several different approaches.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":"265 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82494848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study how the maximal dilatation of the Douady–Earle extension near the origin is controlled by the distortion of the boundary map on finitely many points. Consider the case of points evenly spread on the circle. We show that the maximal dilatation of the extension in a neighborhood of the origin has an upper bound only depending on the cross-ratio distortion of the boundary map on these points if and only if the number n of the points is more than 4. Furthermore, we show that the size of the neighborhood is universal for each n ≥ 5 in the sense that its size only depends on the distortion.
{"title":"Cross-ratio distortion and Douady–Earle extension: III. How to control the dilatation near the origin","authors":"Jun Hu, Oleg Muzician","doi":"10.5186/AASFM.2019.4432","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4432","url":null,"abstract":"In this paper, we study how the maximal dilatation of the Douady–Earle extension near the origin is controlled by the distortion of the boundary map on finitely many points. Consider the case of points evenly spread on the circle. We show that the maximal dilatation of the extension in a neighborhood of the origin has an upper bound only depending on the cross-ratio distortion of the boundary map on these points if and only if the number n of the points is more than 4. Furthermore, we show that the size of the neighborhood is universal for each n ≥ 5 in the sense that its size only depends on the distortion.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":"12 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78376501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. The tropical Nevanlinna theory in the whole real line R describes value distribution of continuous piecewise linear functions of a real variable with arbitrary real slopes, called tropical meromorphic functions, similarly as value distribution of meromorphic functions of a complex variable is described by the classical Nevanlinna theory in the whole complex plane C. As a tropical counterpart to the Nevanlinna theory in a disc or an annulus centered at the origin, we introduce in this paper a value distribution theory of continuous piecewise linear functions in a symmetric finite open interval (−R,R). The shift operator (difference operator) has a key role in the tropical value distribution theory in R corresponding to the role of the differential operator in the Nevanlinna theory in a subregion of C. However, the affine shift x 7→ x+ c does not operate properly in finite intervals. Therefore, we introduce a shift x 7→ sτ (x) which may be called as the tropical hyperbolic shift. This notion enables us to obtain the quotient estimate m (
{"title":"Tropical meromorphic functions in a finite interval","authors":"I. Laine, K. Tohge","doi":"10.5186/AASFM.2019.4418","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4418","url":null,"abstract":"Abstract. The tropical Nevanlinna theory in the whole real line R describes value distribution of continuous piecewise linear functions of a real variable with arbitrary real slopes, called tropical meromorphic functions, similarly as value distribution of meromorphic functions of a complex variable is described by the classical Nevanlinna theory in the whole complex plane C. As a tropical counterpart to the Nevanlinna theory in a disc or an annulus centered at the origin, we introduce in this paper a value distribution theory of continuous piecewise linear functions in a symmetric finite open interval (−R,R). The shift operator (difference operator) has a key role in the tropical value distribution theory in R corresponding to the role of the differential operator in the Nevanlinna theory in a subregion of C. However, the affine shift x 7→ x+ c does not operate properly in finite intervals. Therefore, we introduce a shift x 7→ sτ (x) which may be called as the tropical hyperbolic shift. This notion enables us to obtain the quotient estimate m (","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":"6 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73412703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Boundary growth of generalized Riesz potentials on the unit ball in the variable settings","authors":"Y. Mizuta, T. Ohno, T. Shimomura","doi":"10.5186/aasfm.2019.4403","DOIUrl":"https://doi.org/10.5186/aasfm.2019.4403","url":null,"abstract":"","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":"58 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74732971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Alternative proof of Keith–Zhong self-improvement and connectivity","authors":"Sylvester Eriksson-Pique","doi":"10.5186/AASFM.2019.4424","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4424","url":null,"abstract":"","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":"12 1","pages":"407-425"},"PeriodicalIF":0.9,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73308384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many authors have studied sets, associated with the dynamics of a transcendental entire function, which have the topological property of being a spider's web. In this paper we adapt the definition of a spider's web to the punctured plane. We give several characterisations of this topological structure, and study the connection with the usual spider's web in $mathbb{C}$. We show that there are many transcendental self-maps of $mathbb{C}^*$ for which the Julia set is such a spider's web, and we construct the first example of a transcendental self-map of $mathbb{C}^*$ for which the escaping set $I(f)$ is such a spider's web. By way of contrast with transcendental entire functions, we conjecture that there is no transcendental self-map of $mathbb{C}^*$ for which the fast escaping set $A(f)$ is such a spider's web.
{"title":"Spiders' webs in the punctured plane","authors":"V. Evdoridou, David Mart'i-Pete, D. Sixsmith","doi":"10.5186/aasfm.2020.4528","DOIUrl":"https://doi.org/10.5186/aasfm.2020.4528","url":null,"abstract":"Many authors have studied sets, associated with the dynamics of a transcendental entire function, which have the topological property of being a spider's web. In this paper we adapt the definition of a spider's web to the punctured plane. We give several characterisations of this topological structure, and study the connection with the usual spider's web in $mathbb{C}$. \u0000We show that there are many transcendental self-maps of $mathbb{C}^*$ for which the Julia set is such a spider's web, and we construct the first example of a transcendental self-map of $mathbb{C}^*$ for which the escaping set $I(f)$ is such a spider's web. By way of contrast with transcendental entire functions, we conjecture that there is no transcendental self-map of $mathbb{C}^*$ for which the fast escaping set $A(f)$ is such a spider's web.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":"36 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89218888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give a fundament for Berezin's analytic $Psi$do considered in cite{Berezin71} in terms of Bargmann images of Pilipovi{'c} spaces. We deduce basic continuity results for such $Psi$do, especially when the operator kernels are in suitable mixed weighted Lebesgue spaces and act on certain weighted Lebesgue spaces of entire functions. In particular, we show how these results imply well-known continuity results for real $Psi$do with symbols in modulation spaces, when acting on other modulation spaces.
{"title":"Pseudo-differential calculus in a Bargmann setting","authors":"N. Teofanov, J. Toft","doi":"10.5186/aasfm.2020.4512","DOIUrl":"https://doi.org/10.5186/aasfm.2020.4512","url":null,"abstract":"We give a fundament for Berezin's analytic $Psi$do considered in cite{Berezin71} in terms of Bargmann images of Pilipovi{'c} spaces. We deduce basic continuity results for such $Psi$do, especially when the operator kernels are in suitable mixed weighted Lebesgue spaces and act on certain weighted Lebesgue spaces of entire functions. In particular, we show how these results imply well-known continuity results for real $Psi$do with symbols in modulation spaces, when acting on other modulation spaces.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":"8 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90309216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the regularity of semi-stable, radially symmetric, and decreasing solutions for a class of quasilinear reaction-diffusion equations in the inhomogeneous context of Riemannian manifolds. We prove uniform boundedness, Lebesgue and Sobolev estimates for this class of solutions for equations involving the p-Laplace Beltrami operator and locally Lipschitz non-linearity. We emphasize that our results do not depend on the boundary conditions and the specific form of the non-linearities and metric. Moreover, as an application, we establish regularity of the extremal solutions for equations involving the p-Laplace Beltrami operator with zero Dirichlet boundary conditions.
{"title":"Regularity of stable solutions to quasilinear elliptic equations on Riemannian models","authors":"'O JoaoMarcosdo, R. Clemente","doi":"10.5186/AASFM.2019.4448","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4448","url":null,"abstract":"We investigate the regularity of semi-stable, radially symmetric, and decreasing solutions for a class of quasilinear reaction-diffusion equations in the inhomogeneous context of Riemannian manifolds. We prove uniform boundedness, Lebesgue and Sobolev estimates for this class of solutions for equations involving the p-Laplace Beltrami operator and locally Lipschitz non-linearity. We emphasize that our results do not depend on the boundary conditions and the specific form of the non-linearities and metric. Moreover, as an application, we establish regularity of the extremal solutions for equations involving the p-Laplace Beltrami operator with zero Dirichlet boundary conditions.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":"119 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74870066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：