We extend the notion of a pseudoholomorphic vector of Iwaniec, Verchota, and Vogel to mappings between Riemannian manifolds. Since this class of mappings contains both quasiregular mappings and (pseudo)holomorphic curves, we call them quasiregular curves. Let $nle m$ and let $M$ be an oriented Riemannian $n$-manifold, $N$ a Riemannian $m$-manifold, and $omega in Omega^n(N)$ a smooth closed non-vanishing $n$-form on $N$. A continuous Sobolev map $fcolon M to N$ in $W^{1,n}_{mathrm{loc}}(M,N)$ is a $K$-quasiregular $omega$-curve for $Kge 1$ if $f$ satisfies the distortion inequality $(lVertomegarVertcirc f)lVert DfrVert^n le K (star f^* omega)$ almost everywhere in $M$. We prove that quasiregular curves satisfy Gromov's quasiminimality condition and a version of Liouville's theorem stating that bounded quasiregular curves $mathbb R^n to mathbb R^m$ are constant. We also prove a limit theorem that a locally uniform limit $fcolon M to N$ of $K$-quasiregular $omega$-curves $(f_j colon Mto N)$ is also a $K$-quasiregular $omega$-curve. We also show that a non-constant quasiregular $omega$-curve $fcolon M to N$ is discrete and satisfies $star f^*omega >0$ almost everywhere, if one of the following additional conditions hold: the form $omega$ is simple or the map $f$ is $C^1$-smooth.
我们将Iwaniec, Verchota和Vogel的伪全纯向量的概念推广到黎曼流形之间的映射。由于这类映射既包含拟正则映射又包含(伪)全纯曲线，我们称它们为拟正则曲线。让 $nle m$ 让 $M$ 做一个有方向的黎曼人 $n$-歧管; $N$ 一个黎曼量 $m$-歧管，和 $omega in Omega^n(N)$ 光滑闭合不消失 $n$-form on $N$． 一个连续的Sobolev图 $fcolon M to N$ 在 $W^{1,n}_{mathrm{loc}}(M,N)$ 是? $K$-拟正则 $omega$-曲线 $Kge 1$ 如果 $f$ 满足畸变不等式 $(lVertomegarVertcirc f)lVert DfrVert^n le K (star f^* omega)$ 几乎所有地方 $M$． 证明了拟正则曲线满足Gromov的拟极小性条件和Liouville定理的一个版本，证明了拟正则曲线是有界的 $mathbb R^n to mathbb R^m$ 都是常数。我们还证明了一个局部一致极限的极限定理 $fcolon M to N$ 的 $K$-拟正则 $omega$-曲线 $(f_j colon Mto N)$ 也是一个 $K$-拟正则 $omega$-曲线。我们也证明了一个非常数的拟正则 $omega$-曲线 $fcolon M to N$ 是离散的并且满足 $star f^*omega >0$ 几乎在任何地方，如果下列附加条件之一成立 $omega$ 是简单还是地图 $f$ 是 $C^1$-平滑。
{"title":"Quasiregular curves","authors":"Pekka Pankka","doi":"10.5186/aasfm.2020.4534","DOIUrl":"https://doi.org/10.5186/aasfm.2020.4534","url":null,"abstract":"We extend the notion of a pseudoholomorphic vector of Iwaniec, Verchota, and Vogel to mappings between Riemannian manifolds. Since this class of mappings contains both quasiregular mappings and (pseudo)holomorphic curves, we call them quasiregular curves. Let $nle m$ and let $M$ be an oriented Riemannian $n$-manifold, $N$ a Riemannian $m$-manifold, and $omega in Omega^n(N)$ a smooth closed non-vanishing $n$-form on $N$. A continuous Sobolev map $fcolon M to N$ in $W^{1,n}_{mathrm{loc}}(M,N)$ is a $K$-quasiregular $omega$-curve for $Kge 1$ if $f$ satisfies the distortion inequality $(lVertomegarVertcirc f)lVert DfrVert^n le K (star f^* omega)$ almost everywhere in $M$. We prove that quasiregular curves satisfy Gromov's quasiminimality condition and a version of Liouville's theorem stating that bounded quasiregular curves $mathbb R^n to mathbb R^m$ are constant. We also prove a limit theorem that a locally uniform limit $fcolon M to N$ of $K$-quasiregular $omega$-curves $(f_j colon Mto N)$ is also a $K$-quasiregular $omega$-curve. We also show that a non-constant quasiregular $omega$-curve $fcolon M to N$ is discrete and satisfies $star f^*omega >0$ almost everywhere, if one of the following additional conditions hold: the form $omega$ is simple or the map $f$ is $C^1$-smooth.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76379633","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 obtain symmetrization inequalities on probability metric spaces with convex isoperimetric profile which incorporate in their formulation the isoperimetric estimator and that can be applied to provide a unified treatment of sharp Sobolev-Poincare and Nash inequalities.
{"title":"Symmetrization inequalities for probability metric spaces with convex isoperimetric profile","authors":"Joaquim Martín, Walter A. Ortiz","doi":"10.5186/aasfm.2020.4548","DOIUrl":"https://doi.org/10.5186/aasfm.2020.4548","url":null,"abstract":"We obtain symmetrization inequalities on probability metric spaces with convex isoperimetric profile which incorporate in their formulation the isoperimetric estimator and that can be applied to provide a unified treatment of sharp Sobolev-Poincare and Nash inequalities.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80574773","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}
By means of a counter-example we show that the multilinear fractional operator is not bounded from a product of Hardy spaces into a Hardy space.
通过一个反例证明了多线性分数算子从Hardy空间的积到Hardy空间的无界性。
{"title":"Multilinear fractional integral operators: a counter-example","authors":"P. Rocha","doi":"10.5186/aasfm.2020.4549","DOIUrl":"https://doi.org/10.5186/aasfm.2020.4549","url":null,"abstract":"By means of a counter-example we show that the multilinear fractional operator is not bounded from a product of Hardy spaces into a Hardy space.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76692164","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 problem of the convergence in variation for the generalized sampling series based upon averaged-type kernels in the multidimensional setting. As a crucial tool, we introduce a family of operators of sampling-Kantorovich type for which we prove convergence in L^p on a subspace of L^p(R^N): therefore we obtain the convergence in variation for the multidimensional generalized sampling series by means of a relation between the partial derivatives of such operators acting on an absolutely continuous function f and the sampling-Kantorovich type operators acting on the partial derivatives of f. Applications to digital image processing are also furnished.
{"title":"Convergence in variation for the multidimensional generalized sampling series and applications to smoothing for digital image processing","authors":"L. Angeloni, D. Costarelli, G. Vinti","doi":"10.5186/aasfm.2020.4532","DOIUrl":"https://doi.org/10.5186/aasfm.2020.4532","url":null,"abstract":"In this paper we study the problem of the convergence in variation for the generalized sampling series based upon averaged-type kernels in the multidimensional setting. As a crucial tool, we introduce a family of operators of sampling-Kantorovich type for which we prove convergence in L^p on a subspace of L^p(R^N): therefore we obtain the convergence in variation for the multidimensional generalized sampling series by means of a relation between the partial derivatives of such operators acting on an absolutely continuous function f and the sampling-Kantorovich type operators acting on the partial derivatives of f. Applications to digital image processing are also furnished.","PeriodicalId":50787,"journal":{"name":"Annales Academiae Scientiarum Fennicae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2019-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79006237","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":"Characterizing hyperelliptic surfaces in terms of closed geodesics","authors":"D. Gallo","doi":"10.5186/AASFM.2019.4450","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4450","url":null,"abstract":"","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":"78841243","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":"Nonlinear nonhomogeneous Robin problems with convection","authors":"P. Candito, L. Gasiński, N. Papageorgiou","doi":"10.5186/AASFM.2019.4438","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4438","url":null,"abstract":"","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":"88318580","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}
Let BX be a bounded symmetric domain realized as the unit ball of an ndimensional JB∗-triple X = (C, ‖ · ‖X). In this paper, we give a new definition of Bloch type mappings on BX and give distortion theorems for Bloch type mappings on BX . When BX is the Euclidean unit ball in C, this new definition coincides with that given by Chen and Kalaj or by the author. As a corollary of the distortion theorem, we obtain the lower estimate for the radius of the largest schlicht ball in the image of f centered at f(0) for α-Bloch mappings f on BX . Next, as another corollary of the distortion theorem, we show the Lipschitz continuity of (detB(z, z))1/2n| detDf(z)|1/n for Bloch type mappings f on BX with respect to the Kobayashi metric, where B(z, z) is the Bergman operator on X , and use it to give a sufficient condition for the composition operator Cφ to be bounded from below on the Bloch type space on BX , where φ is a holomorphic self mapping of BX . In the case BX = B , we also give a necessary condition for Cφ to be bounded from below which is a converse to the above result. Finally, as another application of the Lipschitz continuity, we obtain a result related to the interpolating sequences for the Bloch type space on BX .
{"title":"Distortion theorems, Lipschitz continuity and their applications for Bloch type mappings on bounded symmetric domains in C^n","authors":"H. Hamada","doi":"10.5186/AASFM.2019.4451","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4451","url":null,"abstract":"Let BX be a bounded symmetric domain realized as the unit ball of an ndimensional JB∗-triple X = (C, ‖ · ‖X). In this paper, we give a new definition of Bloch type mappings on BX and give distortion theorems for Bloch type mappings on BX . When BX is the Euclidean unit ball in C, this new definition coincides with that given by Chen and Kalaj or by the author. As a corollary of the distortion theorem, we obtain the lower estimate for the radius of the largest schlicht ball in the image of f centered at f(0) for α-Bloch mappings f on BX . Next, as another corollary of the distortion theorem, we show the Lipschitz continuity of (detB(z, z))1/2n| detDf(z)|1/n for Bloch type mappings f on BX with respect to the Kobayashi metric, where B(z, z) is the Bergman operator on X , and use it to give a sufficient condition for the composition operator Cφ to be bounded from below on the Bloch type space on BX , where φ is a holomorphic self mapping of BX . In the case BX = B , we also give a necessary condition for Cφ to be bounded from below which is a converse to the above result. Finally, as another application of the Lipschitz continuity, we obtain a result related to the interpolating sequences for the Bloch type space on BX .","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":"87191736","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":"Existence of weak solutions for the Schrödinger equation and its application","authors":"Jinjin Huang","doi":"10.5186/AASFM.2019.4452","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4452","url":null,"abstract":"","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":"81529897","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. In this paper, we consider the moment of the products of primitive Dirichlet Lfunctions and L-functions associated with a Hecke–Maass form of SL(2,Z) twisted by primitive Dirichlet characters. We prove that for any Hecke–Maass form f of SL(2,Z) and s0 = σ0 + it0 with 1/2 ≤ σ0 < 1, L(s0, f ⊗ χ)L(s0, χ) 6= 0 holds for some primitive Dirichlet character χ if the conductor of χ is prime and sufficiently large. In particular, we show that unconditionally L(1/2+ it, f⊗χ)L(1/2+ it, χ) 6= 0 for some primitive Dirichlet character modulo q for prime values of q satisfying q ≫ (1 + |t|)255+ǫ. If we assume the Ramanujan–Petersson conjecture, the same statement is valid for any prime values of q such that q ≫ (1 + |t|)15+ǫ.
{"title":"Simultaneous nonvanishing of Dirichlet L-functions and twists of Hecke–Maass L-functions in the critical strip","authors":"Keiju Sono","doi":"10.5186/AASFM.2019.4464","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4464","url":null,"abstract":"Abstract. In this paper, we consider the moment of the products of primitive Dirichlet Lfunctions and L-functions associated with a Hecke–Maass form of SL(2,Z) twisted by primitive Dirichlet characters. We prove that for any Hecke–Maass form f of SL(2,Z) and s0 = σ0 + it0 with 1/2 ≤ σ0 < 1, L(s0, f ⊗ χ)L(s0, χ) 6= 0 holds for some primitive Dirichlet character χ if the conductor of χ is prime and sufficiently large. In particular, we show that unconditionally L(1/2+ it, f⊗χ)L(1/2+ it, χ) 6= 0 for some primitive Dirichlet character modulo q for prime values of q satisfying q ≫ (1 + |t|)255+ǫ. If we assume the Ramanujan–Petersson conjecture, the same statement is valid for any prime values of q such that q ≫ (1 + |t|)15+ǫ.","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":"76724888","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 are concerned with existence of positive solution to the class of nonlinear problems of the Kirchhoff type given by Lǫ(u) = H(u− β)f(u) + u 2 ∗ −1 in R , u ∈ H(R ) ∩W 2, q q−1 (R ), where N ≥ 3, q ∈ (2, 2∗), ǫ, β > 0 are positive parameters, f : R → R is a continuous function, H is the Heaviside function, i.e., H(t) = 0 if t ≤ 0, H(t) = 1 if t > 0 and Lǫ(u) := [ M ( 1 ǫN−2 ˆ
在本文中,我们所关心的存在正解的一类非线性问题基尔霍夫类型由Lǫ(u) = H (u−β)f (u) + u 2∗−1 R u∈H (R)∩W 2 q q−1 (R),其中N≥3,问∈(2,2∗),ǫ,β> 0是积极的参数,f:→R是一个连续函数,H是亥维赛函数,也就是说,H (t) = 0如果t≤0 H (t) = 1如果t > 0和Lǫ(u): = [M(1ǫN−2ˆ
{"title":"Existence of positive solution for Kirchhoff type problem with critical discontinuous nonlinearity","authors":"G. Figueiredo, G. G. Santos","doi":"10.5186/AASFM.2019.4453","DOIUrl":"https://doi.org/10.5186/AASFM.2019.4453","url":null,"abstract":"In this paper we are concerned with existence of positive solution to the class of nonlinear problems of the Kirchhoff type given by Lǫ(u) = H(u− β)f(u) + u 2 ∗ −1 in R , u ∈ H(R ) ∩W 2, q q−1 (R ), where N ≥ 3, q ∈ (2, 2∗), ǫ, β > 0 are positive parameters, f : R → R is a continuous function, H is the Heaviside function, i.e., H(t) = 0 if t ≤ 0, H(t) = 1 if t > 0 and Lǫ(u) := [ M ( 1 ǫN−2 ˆ","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":"75636040","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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