QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS

doi:10.1007/s10473-019-0417-x

Abstract

Abstract: In this article, the authors consider the weighted bounds for the singular integral operator defined by

where Ω is homogeneous of degree zero and has vanishing moment of order one, and A is a function on Rⁿ such that ▽A ∈ BMO(Rⁿ). By sparse domination, the authors obtain some quantitative weighted bounds for T_A when Ω satisfies regularity condition of L^r-Dini type for some r ∈ (1, ∞).

Key words: Singular integral operator, sparse domination, A_p constant, maximal operator

CLC Number:

42B20

Wenhua GAO, Guoen HU. QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS[J].Acta mathematica scientia,Series B, 2019, 39(4): 1149-1162.

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