On commutators of Marcinkiewicz integrals with rough kernel

By Yong Ding, Shan-zhen Lu, K. Yabuta. 2002

81 citations recorded by the source corpus.

Abstract In this note we prove that the higher-order commutators μ m Ω,b , μ ∗,m Ω,λ,b and μ m Ω,S,b are all of bounded operators on the weighted L p spaces. These commutators are formed respectively by a BMO ( R n ) function b ( x ) and a class of rough Marcinkiewicz integral operators μ Ω , μ ∗ Ω,λ and μ Ω,S , which are corresponding to the Littlewood–Paley g -function, Littlewood–Paley g ∗ λ -function and the Lusin area integral, respectively. The results in this paper are essential improvements and extensions of the results by Torchinsky and Wang (1990) and by Alvarez et al. (1993).

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5e63191e42581f75a943b9a0fcbfd01c6eb6b4c1

Citations in the corpus

• Intrinsic square functions on the weighted Morrey spaces (2011, unknown): “ng the above estimates for I1 and I2 and taking the supremum over all balls B⊆ Rn, we complete the proof of Theorem 1.1. Given a real-valued function b∈ BMO(Rn), we shall follow the idea developed in [2, 4] and denote F(ξ) = eξ[ b(x)− z)], ξ∈ C. Then by the analyticity of F(ξ) on Cand the Cauchy int”