Boundedness of Calder�n-Zygmund operators on weighted product hardy spaces

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/109164

Title:	Boundedness of Calder�n-Zygmund operators on weighted product hardy spaces
Authors:	李明憶;LEE, MING-YI
Contributors:	理學院數學系
Keywords:	Dyadics;Mathematical functions;Mathematical integrals;Mathematical theorems;Rectangles;Urelements
Date:	2014-01-01
Issue Date:	2026-04-23 16:11:27 (UTC+8)
Publisher:	Theta Foundation
Abstract:	摘要： Let T be a singular integral operator in Journé's class with regularity exponent ε, w ∈ Aq, 1 ≤ q < 1 + ε, and q/(1 + ε) < p ≤ 1. We obtain the ${\mathrm{H}}_{\mathrm{w}}^{\mathrm{p}}(\mathrm{\mathbb{R}}\times \mathrm{\mathbb{R}})-{\mathrm{L}}_{\mathrm{w}}^{\mathrm{p}}\left({\mathrm{\mathbb{R}}}^{2}\right)$ boundedness of T by using R. Fefferman's "trivial lemma" and Journé's covering lemma. Also, using the vector-valued version of the "trivial lemma" and Littlewood–Paley theory, we prove the ${\mathrm{H}}_{\mathrm{w}}^{\mathrm{p}}(\mathrm{\mathbb{R}}\times \mathrm{\mathbb{R}})$-boundedness of T provided ${\mathrm{T}}_{1}^{}\left(1\right)={\mathrm{T}}_{2}^{}\left(1\right)=00$; that is, the reduced T1 theorem on ${\mathrm{H}}_{\mathrm{w}}^{\mathrm{p}}(\mathrm{\mathbb{R}}\times \mathrm{\mathbb{R}})$. In order to show these two results, we demonstrate a new atomic decomposition of ${\mathrm{H}}_{\mathrm{w}}^{\mathrm{p}}(\mathrm{\mathbb{R}}\times \mathrm{\mathbb{R}})\cap {\mathrm{L}}_{\mathrm{w}}^{2}\left({\mathrm{\mathbb{R}}}^{2}\right)$, for which the series converges in ${\mathrm{L}}_{\mathrm{w}}^{2}$. Moreover, a fundamental principle that the boundedness of operators on the weighted product Hardy space can be obtained simply by the actions of such operators on all atoms is given. 出版者： Theta Foundation 出版日期： 2014-08 出處： Journal of operator theory, 2014-08, Vol.72 (1), p.115-133 資源來源： JSTOR Arts & Sciences XV 版權： Copyright © 2014 Theta 識別號： ISSN: 0379-4024 識別號： EISSN: 1841-7744 識別號： DOI: 10.7900/jot.2012nov06.1993
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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