Sharp Cesàro Convergence in the Hardy Spaces Revisited

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

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish
Article number290
JournalJournal of Geometric Analysis
Volume33
Issue number9
DOIs
StatePublished - Sep 2023

Keywords

  • Bergman space
  • Cesàro polynomial
  • Hardy space
  • Norm convergence
  • Taylor polynomial

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