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Properties of Besov and $Q_p$ spaces in terms of the Schwarzian derivative of harmonic mappings 从谐波映射的施瓦兹导数看贝索夫和 $Q_p$ 空间的性质
arXiv - MATH - Complex Variables Pub Date : 2024-08-17 DOI: arxiv-2408.09062
Hugo Arbeláez, Rodrigo Hernández, Willy Sierra
{"title":"Properties of Besov and $Q_p$ spaces in terms of the Schwarzian derivative of harmonic mappings","authors":"Hugo Arbeláez, Rodrigo Hernández, Willy Sierra","doi":"arxiv-2408.09062","DOIUrl":"https://doi.org/arxiv-2408.09062","url":null,"abstract":"In this paper we give a characterization of $log J_f$ belongs to\u0000$widetilde{mathcal{B}}_p$ or $widetilde{mathcal{Q}}_p$ spaces for any\u0000locally univalent sense-preserving harmonic mappings $f$ defined in the unit\u0000disk, using the Schwarzian derivative of $f$ and Carleson meseaure. In\u0000addition, we introduce the classes $mathcal{BT}_p$ and $mathcal{QT}_p$, based\u0000on the Jacobian operator, and begin a study of these.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Generalized Ramanujan Master Theorem and Integral Representation of Meromorphic Functions 广义拉马努詹主定理和同调函数的积分表示法
arXiv - MATH - Complex Variables Pub Date : 2024-08-16 DOI: arxiv-2408.08725
Zachary P. Bradshaw, Omprakash Atale
{"title":"A Generalized Ramanujan Master Theorem and Integral Representation of Meromorphic Functions","authors":"Zachary P. Bradshaw, Omprakash Atale","doi":"arxiv-2408.08725","DOIUrl":"https://doi.org/arxiv-2408.08725","url":null,"abstract":"Ramanujan's Master Theorem is a decades-old theorem in the theory of Mellin\u0000transforms which has wide applications in both mathematics and high energy\u0000physics. The unconventional method of Ramanujan in his proof of the theorem\u0000left convergence issues which were later settled by Hardy. Here we extend\u0000Ramanujan's theorem to meromorphic functions with poles of arbitrary order and\u0000observe that the new theorem produces analogues of Ramanujan's famous theorem.\u0000Moreover, we find that the theorem produces integral representations for\u0000meromorphic functions which are shown to satisfy interesting properties,\u0000opening up an avenue for further study.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Certain Subclass of Harmonic Multivalent Functions Defined by New Linear Operator 新线性算子定义的某些谐波多价函数子类
arXiv - MATH - Complex Variables Pub Date : 2024-08-15 DOI: arxiv-2408.08103
Ali H. Maran, Abdul Rahman S. Juma, Raheam A. Al-Saphory
{"title":"Certain Subclass of Harmonic Multivalent Functions Defined by New Linear Operator","authors":"Ali H. Maran, Abdul Rahman S. Juma, Raheam A. Al-Saphory","doi":"arxiv-2408.08103","DOIUrl":"https://doi.org/arxiv-2408.08103","url":null,"abstract":"This current article aims to study a new subclass of meromorphic functions\u0000with positive coefficients by reconstructing a new operator in the punctured\u0000open disc. Also, some geometric properties are considered and investigated,\u0000such results as coefficient estimates, distortion and growth theorems, radius\u0000of starlikeness, convexity and close to convexity, extreme points, convex\u0000linear combinations, neighbourhoods, and integral transforms for a new class.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Directional Chebyshev Constants on the Boundary 边界上的方向性切比雪夫常数
arXiv - MATH - Complex Variables Pub Date : 2024-08-14 DOI: arxiv-2408.07619
Thomas Bloom, Norman Levenberg
{"title":"Directional Chebyshev Constants on the Boundary","authors":"Thomas Bloom, Norman Levenberg","doi":"arxiv-2408.07619","DOIUrl":"https://doi.org/arxiv-2408.07619","url":null,"abstract":"We prove results on existence of limits in the definition of (weighted)\u0000directional Chebyshev constants at all points of the standard simplex $Sigma\u0000subset {bf R}^d$ for (locally) regular compact sets $Ksubset {bf C}^d$.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Complex $m$-Hessian type equations in weighted energy classes of $m$-subharmonic functions with given boundary value 具有给定边界值的 $m$ 次谐函数加权能级中的复杂 $m$-Hessian 型方程
arXiv - MATH - Complex Variables Pub Date : 2024-08-14 DOI: arxiv-2408.07528
Nguyen Van Phu, Nguyen Quang Dieu
{"title":"Complex $m$-Hessian type equations in weighted energy classes of $m$-subharmonic functions with given boundary value","authors":"Nguyen Van Phu, Nguyen Quang Dieu","doi":"arxiv-2408.07528","DOIUrl":"https://doi.org/arxiv-2408.07528","url":null,"abstract":"In this paper, we concern with the existence of solutions of the complex\u0000$m-$Hessian type equation $-chi(u)H_{m}(u)=mu$ in the class\u0000$mathcal{E}_{m,chi}(f,Omega)$ if there exists subsolution in this class,\u0000where the given boundary value $finmathcal{N}_m(Omega)cap MSH_m(Omega).$","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gabriel's problem for harmonic Hardy spaces 谐波哈代空间的加布里埃尔问题
arXiv - MATH - Complex Variables Pub Date : 2024-08-13 DOI: arxiv-2408.06623
Suman Das
{"title":"Gabriel's problem for harmonic Hardy spaces","authors":"Suman Das","doi":"arxiv-2408.06623","DOIUrl":"https://doi.org/arxiv-2408.06623","url":null,"abstract":"We obtain inequalities of the form $$int_C |f(z)|^p |dz| leq A(p)\u0000int_{mathbb{T}} |f(z)|^p |dz|, quad (p>1)$$ where $f$ is harmonic in the\u0000unit disk $mathbb{D}$, $mathbb{T}$ is the unit circle, and $C$ is any convex\u0000curve in $mathbb{D}$. Such inequalities were originally studied for analytic\u0000functions by R. M. Gabriel [Proc. London Math. Soc. (2), 28(2):121-127, 1928].\u0000We show that these results, unlike in the case of analytic functions, cannot be\u0000true in general for $0< p le 1$. Therefore, we produce an inequality of a\u0000slightly different type, which deals with the case $0<p<1$. An example is given\u0000to show that this result is \"best possible\", in the sense that an extension to\u0000$p=1$ fails. Finally, we consider the special case when $C$ is a circle and\u0000prove a refined result which, surprisingly, holds for $p=1$ as well.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Non-Archimedean Second Main Theorem for Hypersurfaces in Subgeneral Position 次一般位置超曲面的非阿基米德第二主定理
arXiv - MATH - Complex Variables Pub Date : 2024-08-13 DOI: arxiv-2408.07210
Ta Thi Hoai An, William Cherry, Nguyen Viet Phuong
{"title":"A Non-Archimedean Second Main Theorem for Hypersurfaces in Subgeneral Position","authors":"Ta Thi Hoai An, William Cherry, Nguyen Viet Phuong","doi":"arxiv-2408.07210","DOIUrl":"https://doi.org/arxiv-2408.07210","url":null,"abstract":"We apply an idea of Levin to obtain a non-truncated second main theorem for\u0000non-Archimedean analytic maps approximating algebraic hypersurfaces in\u0000subgeneral position. In some cases, for example when all the hypersurfaces are\u0000non-linear and all the intersections are transverse, this improves an\u0000inequality of Quang, whose inequality is sharp for the case of hyperplanes in\u0000subgeneral position.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weighted Yosida Mappings of Several Complex Variables 多个复杂变量的加权约西达映射
arXiv - MATH - Complex Variables Pub Date : 2024-08-13 DOI: arxiv-2408.06800
Nikhil Bharti, Nguyen Van Thin
{"title":"Weighted Yosida Mappings of Several Complex Variables","authors":"Nikhil Bharti, Nguyen Van Thin","doi":"arxiv-2408.06800","DOIUrl":"https://doi.org/arxiv-2408.06800","url":null,"abstract":"Let $M$ be a complete complex Hermitian manifold with metric $E_{M}$ and let\u0000$varphi: [0,infty)rightarrow (0,infty)$ be positive function such that\u0000$$gamma_r=suplimits_{rleq\u0000a<b}left|(varphi(a)-varphi(b))/(a-b)right|leq C,~rin (0,infty),$$ for\u0000some $Cin (0,1],$ and $lim_{rrightarrowinfty}gamma_r=0.$ A holomorphic\u0000mapping $f:mathbb{C}^{m}rightarrow M$ is said to be a weighted Yosida mapping\u0000if for any $z,~xiinmathbb{C}^{m}$ with $|xi|=1,$ the quantity\u0000$varphi(|z|)E_{M}(f(z), df(z)(xi))$ remains bounded above, where $df(z)$ is\u0000the map from $T_z(mathbb{C}^{m})$ to $T_{f(z)}(M)$ induced by $f.$ We present\u0000several criteria of holomorphic mappings belonging to the class of all weighted\u0000Yosida mappings.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"314 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lappan's five-point theorem for φ-Normal Harmonic Mappings φ正态谐波映射的拉潘五点定理
arXiv - MATH - Complex Variables Pub Date : 2024-08-11 DOI: arxiv-2408.05809
Nisha Bohra, Gopal Datt, Ritesh Pal
{"title":"Lappan's five-point theorem for φ-Normal Harmonic Mappings","authors":"Nisha Bohra, Gopal Datt, Ritesh Pal","doi":"arxiv-2408.05809","DOIUrl":"https://doi.org/arxiv-2408.05809","url":null,"abstract":"A harmonic mapping $f=h+overline{g}$ in $mathbb{D}$ is $varphi$-normal if\u0000$f^{#}(z)=mathcal{O}(|varphi(z)|), text{ as } |z|to 1^-,$ where\u0000$f^{#}(z)={(|h'(z)|+|g'(z)|)}/{(1+|f(z)|^2)}.$ In this paper, we establish\u0000several sufficient conditions for harmonic mappings to be $varphi$-normal. We\u0000also extend the five-point theorem of Lappan for $varphi$-normal harmonic\u0000mappings.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Projective embedding of degenerating family of Kähler-Einstein manifolds of negative curvature 负曲率凯勒-爱因斯坦流形退化族的投影嵌入
arXiv - MATH - Complex Variables Pub Date : 2024-08-09 DOI: arxiv-2408.04824
Jingzhou Sun
{"title":"Projective embedding of degenerating family of Kähler-Einstein manifolds of negative curvature","authors":"Jingzhou Sun","doi":"arxiv-2408.04824","DOIUrl":"https://doi.org/arxiv-2408.04824","url":null,"abstract":"We study the Bergman embeddings of degenerating families of\u0000K\"{a}hler-Einsten manifolds of negative curvature. In one special case, we\u0000show that we can construct orthonormal bases so that the induced Bergman\u0000embeddings converge to the Bergman embedding of the limit space together with\u0000bubbles.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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