Transference and restriction of maximal multiplier operators on Hardy spaces

• Autorzy: Zhixin Liu , Shanzhen Lu
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to establish transference and restriction theorems for maximal operators defined by multipliers on the Hardy spaces $H^p(ℝ^n)$ and $H^p(𝕋^n)$, 0 < p ≤ 1, which generalize the results of Kenig-Tomas for the case p > 1. We prove that under a mild regulation condition, an $L^∞(ℝ^n)$ function m is a maximal multiplier on $H^p(ℝ^n)$ if and only if it is a maximal multiplier on $H^p(𝕋^n)$. As an application, the restriction of maximal multipliers to lower dimensional Hardy spaces is considered.

Kategorie tematyczne

• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 105
• Numer: 2
• Strony: 121-134

Daty

wydano

1993

otrzymano

1991-03-28

poprawiono

1993-01-20

Twórcy

autor

Zhixin Liu

• Department of Applied Mathematics, Tsinghua University, Beijing, 100084, China

autor

Shanzhen Lu

• Department of Mathematics, Beijing Normal University, Beijing, 100875, China

Bibliografia

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