Hadamard Convolution and Area Integral Means in Bergman Spaces

2020 ◽  
Vol 75 (2) ◽  
Author(s):  
Boban Karapetrović ◽  
Javad Mashreghi
Keyword(s):  
Bergman Spaces ◽  
Integral Means ◽  
Area Integral

Area Integral Means of Analytic Functions in the Unit Disk

2018 ◽  
Vol 61 (3) ◽  
pp. 509-517 ◽  
Author(s):  
Xiaohui Cui ◽  
Chunjie Wang ◽  
Kehe Zhu
Keyword(s):  
Analytic Function ◽  
Convex Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Integral Means ◽  
Area Measure ◽  
Area Integral

AbstractFor an analytic function ऒ on the unit disk , we show that the L2 integral mean of ऒ on c < |z| < r with respect to the weighted area measure (1 − |z|2)αd A(z) is a logarithmically convex function of r on (c, 1), where −3 ≤ ∞ ≤ 0 and c ∈ [0, 1). Moreover, the range [−3, 0] for ∞ is best possible. When c = 0, our arguments here also simplify the proof for several results we obtained in earlier papers.

scholarly journals LOGARITHMIC CONVEXITY OF AREA INTEGRAL MEANS FOR ANALYTIC FUNCTIONS II

2014 ◽  
Vol 98 (1) ◽  
pp. 117-128 ◽  
Author(s):  
CHUNJIE WANG ◽  
JIE XIAO ◽  
KEHE ZHU
Keyword(s):  
Analytic Function ◽  
Convex Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Integral Means ◽  
Area Measure ◽  
Logarithmic Convexity ◽  
Area Integral

AbstractFor$0<p<\infty$and$-2\leq {\it\alpha}\leq 0$we show that the$L^{p}$integral mean on$r\mathbb{D}$of an analytic function in the unit disk$\mathbb{D}$with respect to the weighted area measure$(1-|z|^{2})^{{\it\alpha}}\,dA(z)$is a logarithmically convex function of$r$on$(0,1)$.

Area integral means over the annuli

2019 ◽  
Vol 473 (1) ◽  
pp. 510-518 ◽  
Author(s):  
Chunjie Wang ◽  
Wenjie Yang
Keyword(s):  
Integral Means ◽  
Area Integral

Convexity for area integral means

2020 ◽  
Vol 491 (2) ◽  
pp. 124345
Author(s):  
Qinxia Hu ◽  
Chunjie Wang
Keyword(s):  
Integral Means ◽  
Area Integral

scholarly journals Addendum to the Paper “A note on Weighted bergman Spaces and the cesaro operator”

2005 ◽  
Vol 180 ◽  
pp. 77-90 ◽  
Author(s):  
Der-Chen Chang ◽  
Stevo Stević
Keyword(s):  
Bergman Space ◽  
Bergman Spaces ◽  
Holomorphic Functions ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Cesàro Operator ◽  
Integral Means ◽  
Measurable Functions ◽  
Unit Polydisk ◽  
Cesaro Operator

AbstractLet H(Dn) be the space of holomorphic functions on the unit polydisk Dn, and let , where p, q> 0, α = (α1,…,αn) with αj > -1, j =1,..., n, be the class of all measurable functions f defined on Dn such thatwhere Mp(f,r) denote the p-integral means of the function f. Denote the weighted Bergman space on . We provide a characterization for a function f being in . Using the characterization we prove the following result: Let p> 1, then the Cesàro operator is bounded on the space .

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