Lp boundedness for commutators of parabolic Littlewood-Paley operators with rough kernels

✍ Scribed by Dongxiang Chen; Shanzhen Lu

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 166 KB
• Volume: 284
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200810139

✦ Synopsis

Abstract

In this paper, L^p^ bounds for the m‐th order commutators of the parabolic Littlewood‐Paley operator are obtained, provided that the kernel Ω belongs to L(log^+^L)^m + 1/2^(S^n − 1^) or \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$B_q^{0,m-1/2}(S^{n-1})$\end{document} (certain block spaces) for center q > 1,\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$1 < p <\infty , m\in \mathbb {N}$\end{document}. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim