Complex Analysis and Operator Theory最新文献_第6页

Regularity of the Berezin Transform on the Elementary Reinhardt Domains 基本莱因哈特域上的贝雷津变换正则性

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-05-13 DOI: 10.1007/s11785-024-01538-w

Linhe Yang, Qingyang Zou

引用次数: 0

Some Relations Between Schwarz–Pick Inequality and von Neumann’s Inequality 施瓦茨-皮克不等式与冯-诺依曼不等式之间的某些关系

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-05-10 DOI: 10.1007/s11785-024-01526-0

Kenta Kojin

{"title":"Some Relations Between Schwarz–Pick Inequality and von Neumann’s Inequality","authors":"Kenta Kojin","doi":"10.1007/s11785-024-01526-0","DOIUrl":"https://doi.org/10.1007/s11785-024-01526-0","url":null,"abstract":"We study a Schwarz–Pick type inequality for the Schur–Agler class (SA(B_{delta })). In our operator theoretical approach, von Neumann’s inequality for a class of generic tuples of (2times 2) matrices plays an important role rather than holomorphy. In fact, the class (S_{2, gen}(B_{Delta })) consisting of functions that satisfy the inequality for those matrices enjoys $$begin{aligned} d_{mathbb {D}}(f(z), f(w))le d_{Delta }(z, w) ;;(z,win B_{Delta }, fin S_{2, gen}(B_{Delta })). end{aligned}$$Here, (d_{Delta }) is a function defined by a matrix (Delta ) of functions. Later, we focus on the case when (Delta ) is a matrix of holomorphic functions. We use the pseudo-distance (d_{Delta }) to give a sufficient condition on a diagonalizable commuting tuple T acting on (mathbb {C}^2) for (B_{Delta }) to be a complete spectral domain for T. We apply this sufficient condition to generalizing von Neumann’s inequalities studied by Drury (In: Blei RC, Sidney SJ (eds) Banach spaces, harmonic analysis, and probability theory, lecture notes in mathematics, vol 995. Springer, Berlin, pp 14–32, 1983) and by Hartz–Richter–Shalit (Math Z 301:3877–3894, 2022).","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"31 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939104","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}

引用次数: 0

Multivalued Elliptic Inclusion in Fractional Orlicz–Sobolev Spaces 分数 Orlicz-Sobolev 空间中的多值椭圆包容

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-05-09 DOI: 10.1007/s11785-024-01541-1

H. El-Houari, S. Hajar, H. Moussa

引用次数: 0

Hankel-Type Operator Acting on Hardy Spaces and Weighted Bergman Spaces 作用于哈代空间和加权伯格曼空间的汉克尔型算子

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-05-06 DOI: 10.1007/s11785-024-01539-9

Zhihui Zhou

引用次数: 0

Fractional Gamma Noise Functionals 分数伽玛噪声函数

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-05-05 DOI: 10.1007/s11785-024-01534-0

Mohamed Ayadi, Anis Riahi, Mohamed Rhaima, Hamza Ghoudi

引用次数: 0

Limiting Weak-Type Behavior of the Centered Hardy–Littlewood Maximal Function of General Measures on the Positive Real Line 正实线上一般度量的居中哈代-利特尔伍德最大函数的极限弱类型行为

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-05-03 DOI: 10.1007/s11785-024-01533-1

Wu-yi Pan, Sheng-jian Li

{"title":"Limiting Weak-Type Behavior of the Centered Hardy–Littlewood Maximal Function of General Measures on the Positive Real Line","authors":"Wu-yi Pan, Sheng-jian Li","doi":"10.1007/s11785-024-01533-1","DOIUrl":"https://doi.org/10.1007/s11785-024-01533-1","url":null,"abstract":"Given a positive Borel measure (mu ) on the one-dimensional Euclidean space (textbf{R}), consider the centered Hardy–Littlewood maximal function (M_mu ) acting on a finite positive Borel measure (nu ) by $$begin{aligned} M_{mu }nu (x):=sup _{r>r_0(x)}frac{nu (B(x,r))}{mu (B(x,r))},quad hbox { } xin textbf{R}, end{aligned}$$where (r_0(x) = inf {r> 0: mu (B(x,r)) > 0}) and B(x, r) denotes the closed ball with centre x and radius (r > 0). In this note, we restrict our attention to Radon measures (mu ) on the positive real line ([0,+infty )). We provide a complete characterization of measures having weak-type asymptotic properties for the centered maximal function. Although we don’t know whether this fact can be extended to measures on the entire real line (textbf{R}), we examine some criteria for the existence of the weak-type asymptotic properties for (M_mu ) on (textbf{R}). We also discuss further properties, and compute the value of the relevant asymptotic quantity for several examples of measures.\u0000","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"14 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889431","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}

引用次数: 0

A Peak Set of Hausdorff Dimension 2n − 1 for the Algebra A(D) in the Boundary of a Domain D with C⌃2 Boundary 具有 C⌃2 边界的域 D 边界中代数 A(D) 的豪斯多夫维度为 2n - 1 的峰集

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-05-02 DOI: 10.1007/s11785-024-01532-2

Piotr Kot

引用次数: 0

Orthogonal Exponential Functions on the Three-Dimensional Sierpinski Gasket 三维西尔平斯基垫圈上的正交指数函数

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-04-30 DOI: 10.1007/s11785-024-01536-y

Zhi-Min Wang

{"title":"Orthogonal Exponential Functions on the Three-Dimensional Sierpinski Gasket","authors":"Zhi-Min Wang","doi":"10.1007/s11785-024-01536-y","DOIUrl":"https://doi.org/10.1007/s11785-024-01536-y","url":null,"abstract":"Let (xi in mathbb {R}), and (rho _iin mathbb {R}) with (0<|rho _i|<1) for (1le ile 3). For an expanding real matrix $$begin{aligned} M=begin{bmatrix} rho _1^{-1}&{}0&{}xi 0&{}rho _2^{-1}&{}-xi 0&{}0&{}rho _3^{-1} end{bmatrix}in M_3(mathbb {R}) end{aligned}$$and an integer digit set (D={(0,0,0)^t, (1,0,0)^t, (0,1,0)^t, (0,0,1)^t }subset mathbb {Z}^3), let (mu _{M,D}) be the self-affine measure defined by (mu _{M,D}(cdot )=frac{1}{|D|}sum _{din D}mu _{M,D}(M(cdot )-d)). In this paper, we prove that if (rho _1=rho _2), then (L^2(mu _{M,D})) admits an infinite orthogonal set of exponential functions if and only if (|rho _i|=(p_i/q_i)^{frac{1}{r_i}}) for some (p_i,q_i,r_iin mathbb {N}^+) with (gcd (p_i,q_i)=1) and (2|q_i), (i=1,2). In particular, if (rho _1,rho _2,rho _3in {frac{p}{q}:p,qin 2mathbb {Z}+1}) and (rho _1=rho _2), then there exist at most 4 mutually orthogonal exponential functions in (L^2(mu _{M,D})), and the number 4 is the best.","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"46 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839945","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}

引用次数: 0

Geometric Interpolation in n-Tuples of Noncommutative $$L_p$$ -Spaces 非交换 $$L_p$$ 空间 n 元组中的几何插值

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-04-30 DOI: 10.1007/s11785-024-01535-z

Feng Zhang

引用次数: 0

Almansi-Type Decomposition for Slice Regular Functions of Several Quaternionic Variables 多个四元变量的片正则函数的阿尔曼西式分解

IF 0.8 4区数学

Complex Analysis and Operator Theory Pub Date : 2024-04-29 DOI: 10.1007/s11785-024-01529-x

Giulio Binosi

引用次数: 0