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L p estimates for the commutators of Marcinkiewicz integrals with kernels belonging to certain block spaces
Author(s) -
Wu Huoxiong
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410413
Subject(s) - mathematics , kernel (algebra) , pure mathematics , order (exchange) , block (permutation group theory) , class (philosophy) , function (biology) , fourier transform , mathematical analysis , combinatorics , finance , artificial intelligence , evolutionary biology , computer science , economics , biology
Abstract This paper is devoted to the study of the L p ‐mapping properties of the higher order commutators μ k Ω, a , μ *, kΩ, 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)