Lp estimates for the commutators of Marcinkiewicz integrals with kernels belonging to certain block spaces

✍ Scribed by Huoxiong Wu

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 217 KB
• Volume: 279
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200410413

✦ Synopsis

Abstract

This paper is devoted to the study of the L^p^ ‐mapping properties of the higher order commutators μ ^k^ ~Ω,a~ , μ ^*,k^ ~Ω,λ ,a~ and μ ^k^ ~Ω,S ,a~ , which are formed respectively by a BMO (ℝ^n^ ) function a (x ) and a class of rough Marcinkiewicz integral operators μ ~Ω~, μ ^*^~Ω,λ~ and μ ~Ω,S~ related to the Littlewood–Paley g ‐function, the Littlewood–Paley g ^*^~λ~ ‐function and the Lusin area integral, respectively. By the method of block decomposition for kernel functions and Fourier transforms estimates, some new results about the L^p^ (ℝ^n^ ) boundedness for theses commutators are obtained. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)