In the paper composition operators acting on quasi-Banach spaces of analytic functions on the unit disc of the complex plane are studied. In particular characterizations in terms of a function φ of order bounded as well as summing operators Cφ are presented, if Cφ is an operator from an abstract Hardy space. Applications are shown for the special case of Hardy–Orlicz, Hardy–Lorentz, and growth spaces.
{"title":"Composition operators on Banach spaces of analytic functions","authors":"M. Mastyło, P. Mleczko","doi":"10.5186/AASFM.2019.4436","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4436","url":null,"abstract":"In the paper composition operators acting on quasi-Banach spaces of analytic functions on the unit disc of the complex plane are studied. In particular characterizations in terms of a function φ of order bounded as well as summing operators Cφ are presented, if Cφ is an operator from an abstract Hardy space. Applications are shown for the special case of Hardy–Orlicz, Hardy–Lorentz, and growth spaces.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76388059","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 1985, Robert L. Pego characterized compact families in $L^2(reals)$ in terms of the Fourier transform. It took nearly 30 years to realize that Pego's result can be proved in a wider setting of locally compact abelian groups (works of Gorka and Kostrzewa). In the current paper, we argue that the Fourier transform is not the only integral transform that is efficient in characterizing compact families and suggest the Laplace transform as a possible alternative.
1985年，Robert L. Pego用傅里叶变换描述了L^2(real)$中的紧族。人们花了将近30年的时间才意识到Pego的结果可以在更广泛的局部紧化阿贝尔群(Gorka和Kostrzewa的作品)中得到证明。在当前的论文中，我们认为傅里叶变换并不是唯一有效表征紧族的积分变换，并建议拉普拉斯变换作为一种可能的替代方法。
{"title":"Characterizing compact families via the Laplace transform","authors":"M. Krukowski","doi":"10.5186/aasfm.2020.4553","DOIUrl":"https://doi.org/10.5186/aasfm.2020.4553","url":null,"abstract":"In 1985, Robert L. Pego characterized compact families in $L^2(reals)$ in terms of the Fourier transform. It took nearly 30 years to realize that Pego's result can be proved in a wider setting of locally compact abelian groups (works of Gorka and Kostrzewa). In the current paper, we argue that the Fourier transform is not the only integral transform that is efficient in characterizing compact families and suggest the Laplace transform as a possible alternative.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80673874","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 1994 J. Lewis obtained a purely harmonic proof of the classical Little Picard Theorem by showing that if the joint value distribution of two entire harmonic functions satisfies certain restrictions then they are necessarily constant. We generalize Lewis'theorem and the harmonic Liouville theorem in terms of the range of a harmonic map in the plane.
{"title":"On the range of harmonic maps in the plane","authors":"J. G. Llorente","doi":"10.5186/aasfm.2020.4550","DOIUrl":"https://doi.org/10.5186/aasfm.2020.4550","url":null,"abstract":"In 1994 J. Lewis obtained a purely harmonic proof of the classical Little Picard Theorem by showing that if the joint value distribution of two entire harmonic functions satisfies certain restrictions then they are necessarily constant. We generalize Lewis'theorem and the harmonic Liouville theorem in terms of the range of a harmonic map in the plane.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88547361","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 focus our attention on the notion of intrinsic Lipschitz graphs, inside a special class of metric spaces i.e. the Carnot groups. More precisely, we provide a characterization of locally intrinsic Lipschitz functions in Carnot groups of step 2 in terms of their intrinsic distributional gradients.
{"title":"Intrinsic Lipschitz graphs in Carnot groups of step 2","authors":"D. Donato","doi":"10.5186/aasfm.2020.4556","DOIUrl":"https://doi.org/10.5186/aasfm.2020.4556","url":null,"abstract":"We focus our attention on the notion of intrinsic Lipschitz graphs, inside a special class of metric spaces i.e. the Carnot groups. More precisely, we provide a characterization of locally intrinsic Lipschitz functions in Carnot groups of step 2 in terms of their intrinsic distributional gradients.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84930608","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 study the $L^{p}$-solutions for the semilinear heat equation with unbounded coefficients and driven by a infinite dimensional fractional Brownian motion with self-similarity parameter $H > 1/2$. Existence and uniqueness of local mild solutions are showed.
{"title":"Local L^p-solution for semilinear heat equation with fractional noise","authors":"J. Clarke, C. Olivera","doi":"10.5186/aasfm.2020.4505","DOIUrl":"https://doi.org/10.5186/aasfm.2020.4505","url":null,"abstract":"We study the $L^{p}$-solutions for the semilinear heat equation with unbounded coefficients and driven by a infinite dimensional fractional Brownian motion with self-similarity parameter $H > 1/2$. Existence and uniqueness of local mild solutions are showed.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72385909","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 show that a direct tract bounded by a simple curve is a logarithmic tract and further give sufficient conditions for a direct tract to contain logarithmic tracts. As an application of these results, an example of a function with infinitely many direct singularities, but no logarithmic singularity over any finite value, is shown to be in the Eremenko-Lyubich class.
{"title":"Identifying logarithmic tracts","authors":"James Waterman","doi":"10.5186/aasfm.2020.4543","DOIUrl":"https://doi.org/10.5186/aasfm.2020.4543","url":null,"abstract":"We show that a direct tract bounded by a simple curve is a logarithmic tract and further give sufficient conditions for a direct tract to contain logarithmic tracts. As an application of these results, an example of a function with infinitely many direct singularities, but no logarithmic singularity over any finite value, is shown to be in the Eremenko-Lyubich class.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80276786","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 new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of $L^infty$ atoms, vector-valued inequalities for maximal and other operators, and Rubio de Francia extrapolation. Many of these estimates are not new, but we give new and substantially simpler proofs, which in turn significantly simplifies the proofs of the Hardy spaces inequalities.
给出了加权和变指数Hardy空间上分数和奇异积分算子Hardy空间估计的新证明。我们的证明由几个相互关联的思想组成:根据$L^infty$原子的有限原子分解，极大算子和其他算子的向量值不等式，以及Rubio de Francia外推。这些估计中的许多不是新的，但我们给出了新的和实质上更简单的证明，这反过来又大大简化了哈代空间不等式的证明。
{"title":"A new approach to norm inequalities on weighted and variable Hardy spaces","authors":"D. Cruz-Uribe, Kabe Moen, H. Nguyen","doi":"10.5186/aasfm.2020.4526","DOIUrl":"https://doi.org/10.5186/aasfm.2020.4526","url":null,"abstract":"We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of $L^infty$ atoms, vector-valued inequalities for maximal and other operators, and Rubio de Francia extrapolation. Many of these estimates are not new, but we give new and substantially simpler proofs, which in turn significantly simplifies the proofs of the Hardy spaces inequalities.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78491389","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":"Average box dimensions of typical compact sets","authors":"L. Olsen","doi":"10.5186/AASFM.2019.4406","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4406","url":null,"abstract":"","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81640682","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}
The Teichmüller space of a Riemann surface of analytically finite type has a complex structure modeled on the complex Hilbert space consisting of harmonic Beltrami differentials on the surface equipped with hyperbolic L-norm. The Weil– Petersson metric is an Hermitian metric induced by this Hilbert manifold structure and is studied in many fields. In the complex analysis, Ahlfors [2, 3] proved that the Weil–Petersson metric is a Kähler metric and has the negative holomorphic sectional curvature, negative Ricci curvature and negative scalar curvature. In the hyperbolic geometry, Wolpert [17, 18] gave the several relations between the Weil–Petersson metric and the Fenchel–Nielsen coordinate. In general, that Hilbert manifold structure cannot be introduced to the Teichmüller space of a Riemann surface of analytically infinite type (cf. [9]). Takhtajan and Teo [15] realized this structure as a distribution on the universal Teichmüller space. Cui [5] accomplished the same result on the subset of the universal Teichmüller space independently of Takhtajan and Teo. Hui [6] and Tang [16] extended the argument of Cui to the subset modeled on p-integrable Beltrami differentials for p ≥ 2, which we call the p-integrable Teichmüller space. Later, Radnell, Schippers and Staubach [11, 12, 13] composed a Hilbert manifold structure on a certain refined Teichmüller space of a bordered Riemann surface, which is refered to as the WP-class Teichmüller space. In [5, 15], the Weil–Petersson metric was studied for each Hilbert manifold structure. In particular, it was shown that this metric is negatively curved (cf. [15]) and complete (cf. [5]). Recently, Matsuzaki [8] researched some properties of the p-Weil– Petersson metric on the p-integrable Teichmüller space of the unit disk for p ≥ 2. This metric is a certain extended concept of the Weil–Petersson metric on the square integrable Teichmüller space. In fact, it was proved in [8] that the metric is complete and continuous. Based on their results, the author [19] introduced some complex analytic structure on the p-integrable Teichmüller space of a Riemann surface with Lehner’s condition
{"title":"Smoothness and strongly pseudoconvexity of p-Weil–Petersson metric","authors":"Masahiro Yanagishita","doi":"10.5186/AASFM.2019.4413","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4413","url":null,"abstract":"The Teichmüller space of a Riemann surface of analytically finite type has a complex structure modeled on the complex Hilbert space consisting of harmonic Beltrami differentials on the surface equipped with hyperbolic L-norm. The Weil– Petersson metric is an Hermitian metric induced by this Hilbert manifold structure and is studied in many fields. In the complex analysis, Ahlfors [2, 3] proved that the Weil–Petersson metric is a Kähler metric and has the negative holomorphic sectional curvature, negative Ricci curvature and negative scalar curvature. In the hyperbolic geometry, Wolpert [17, 18] gave the several relations between the Weil–Petersson metric and the Fenchel–Nielsen coordinate. In general, that Hilbert manifold structure cannot be introduced to the Teichmüller space of a Riemann surface of analytically infinite type (cf. [9]). Takhtajan and Teo [15] realized this structure as a distribution on the universal Teichmüller space. Cui [5] accomplished the same result on the subset of the universal Teichmüller space independently of Takhtajan and Teo. Hui [6] and Tang [16] extended the argument of Cui to the subset modeled on p-integrable Beltrami differentials for p ≥ 2, which we call the p-integrable Teichmüller space. Later, Radnell, Schippers and Staubach [11, 12, 13] composed a Hilbert manifold structure on a certain refined Teichmüller space of a bordered Riemann surface, which is refered to as the WP-class Teichmüller space. In [5, 15], the Weil–Petersson metric was studied for each Hilbert manifold structure. In particular, it was shown that this metric is negatively curved (cf. [15]) and complete (cf. [5]). Recently, Matsuzaki [8] researched some properties of the p-Weil– Petersson metric on the p-integrable Teichmüller space of the unit disk for p ≥ 2. This metric is a certain extended concept of the Weil–Petersson metric on the square integrable Teichmüller space. In fact, it was proved in [8] that the metric is complete and continuous. Based on their results, the author [19] introduced some complex analytic structure on the p-integrable Teichmüller space of a Riemann surface with Lehner’s condition","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73474421","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}
Zunwei Fu, Shan-zhen Lu, Hongbin Wang, Liguang Wang
{"title":"Singular integral operators with rough kernels on central Morrey spaces with variable exponent","authors":"Zunwei Fu, Shan-zhen Lu, Hongbin Wang, Liguang Wang","doi":"10.5186/AASFM.2019.4431","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4431","url":null,"abstract":"","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87990474","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}
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