A sparse domination for the Marcinkiewicz integral with rough kernel and applications

2019/05/26 by Tao, Xiangxing, Hu, Guooen
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.10755

Abstract

Let Ω be homogeneous of degree zero, have mean value zero and integrable on the unit sphere, and μ_Ω be the higher-dimensional Marcinkiewicz integral defined by μ_Ω(f)(x)= (∫₀^∞|∫_{|x-y|≤ t}\fracΩ(x-y)|x-y|^n-1f(y)dy|²(dt)/(t³))^1/2. In this paper, the authors establish a bilinear sparse domination for μ_Ω under the assumption Ω∈ L^∞(S^n-1). As applications, some quantitative weighted bounds for μ_Ω are obtained.

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