Sharp Cesàro Convergence in the Hardy Spaces Revisited

Bonan Chen; Guozheng Cheng; Xiang Fang; Chao Liu; Tao Yu

doi:10.1007/s12220-023-01354-2

Sharp Cesàro Convergence in the Hardy Spaces Revisited

Bonan Chen, Guozheng Cheng, Xiang Fang, Chao Liu, Tao Yu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For any f∈ H^p(D) (p> 0) , the Hardy space over the unit disk, we characterize completely the triple (α, p, q) ∈ (- 1 , ∞) × (0 , ∞) ² such that the Cesàro partial sum σnαf converges in norm in H^q(D) , and in the Bergman space Laq(D) , respectively. This extends recent results of McNeal–Xiong and of Park–Zhao–Zhu, and complements a classical theorem of Hardy-Littlewood in 1934.

Original language	English
Article number	290
Journal	Journal of Geometric Analysis
Volume	33
Issue number	9
DOIs	https://doi.org/10.1007/s12220-023-01354-2
State	Published - Sep 2023

Keywords

Bergman space
Cesàro polynomial
Hardy space
Norm convergence
Taylor polynomial

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10.1007/s12220-023-01354-2

Problems in Random Operator Theory(4/4)
Fang, X. (PI)
1/08/22 → 31/07/23
Project: Research

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title = "Sharp Ces{\`a}ro Convergence in the Hardy Spaces Revisited",

abstract = "For any f∈ Hp(D) (p> 0) , the Hardy space over the unit disk, we characterize completely the triple (α, p, q) ∈ (- 1 , ∞) × (0 , ∞) 2 such that the Ces{\`a}ro partial sum σnαf converges in norm in Hq(D) , and in the Bergman space Laq(D) , respectively. This extends recent results of McNeal–Xiong and of Park–Zhao–Zhu, and complements a classical theorem of Hardy-Littlewood in 1934.",

keywords = "Bergman space, Ces{\`a}ro polynomial, Hardy space, Norm convergence, Taylor polynomial",

author = "Bonan Chen and Guozheng Cheng and Xiang Fang and Chao Liu and Tao Yu",

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T1 - Sharp Cesàro Convergence in the Hardy Spaces Revisited

AU - Chen, Bonan

AU - Cheng, Guozheng

AU - Fang, Xiang

AU - Liu, Chao

AU - Yu, Tao

PY - 2023/9

Y1 - 2023/9

N2 - For any f∈ Hp(D) (p> 0) , the Hardy space over the unit disk, we characterize completely the triple (α, p, q) ∈ (- 1 , ∞) × (0 , ∞) 2 such that the Cesàro partial sum σnαf converges in norm in Hq(D) , and in the Bergman space Laq(D) , respectively. This extends recent results of McNeal–Xiong and of Park–Zhao–Zhu, and complements a classical theorem of Hardy-Littlewood in 1934.

AB - For any f∈ Hp(D) (p> 0) , the Hardy space over the unit disk, we characterize completely the triple (α, p, q) ∈ (- 1 , ∞) × (0 , ∞) 2 such that the Cesàro partial sum σnαf converges in norm in Hq(D) , and in the Bergman space Laq(D) , respectively. This extends recent results of McNeal–Xiong and of Park–Zhao–Zhu, and complements a classical theorem of Hardy-Littlewood in 1934.

KW - Bergman space

KW - Cesàro polynomial

KW - Hardy space

KW - Norm convergence

KW - Taylor polynomial

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DO - 10.1007/s12220-023-01354-2

M3 - 期刊論文

AN - SCOPUS:85164202065

SN - 1050-6926

VL - 33

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 9

M1 - 290

ER -

Sharp Cesàro Convergence in the Hardy Spaces Revisited

Abstract

Keywords

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Problems in Random Operator Theory(4/4)

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