Atomic decomposition and boundedness of operators on weighted hardy spaces

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/109158

Title:	Atomic decomposition and boundedness of operators on weighted hardy spaces
Authors:	李明憶;Han, Yongsheng;Lee, Ming-Yi;Lin, Chin-Cheng
Contributors:	理學院數學系
Date:	2012-08-29
Issue Date:	2026-04-23 16:11:01 (UTC+8)
Publisher:	Canadian Mathematical Society;Cambridge, UK: Cambridge University Press
Abstract:	摘要： In this article, we establish a new atomic decomposition for $f\,\in \,L_{w}^{2}\,\bigcap \,H_{w}^{p}$ , where the decomposition converges in $L_{w}^{2}$ -norm rather than in the distribution sense. As applications of this decomposition, assuming that $T$ is a linear operator bounded on $L_{w}^{2}$ and $0\,<\,p\,\le \,1$ , we obtain (i) if $T$ is uniformly bounded in $L_{w}^{p}$ -norm for all $w-p$ -atoms, then $T$ can be extended to be bounded from $H_{w}^{p}$ to $L_{w}^{2}$ ; (ii) if $T$ is uniformly bounded in $H_{w}^{p}$ -norm for all $w-p$ -atoms, then $T$ can be extended to be bounded on $H_{w}^{p}$ ; (iii) if $T$ is bounded on $H_{w}^{p}$ , then $T$ can be extended to be bounded from $H_{w}^{p}$ to $L_{w}^{2}$ . 其他題名： Can. math. bull 出版者： Cambridge, UK: Cambridge University Press 出版日期： 2012-06-01 出處： Canadian mathematical bulletin, 2012-06, Vol.55 (2), p.303-314 版權： Copyright © Canadian Mathematical Society 2012 識別號： ISSN: 0008-4395 識別號： ISSN: 1496-4287 識別號： EISSN: 1496-4287 識別號： DOI: 10.4153/CMB-2011-072-7
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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