Abstract
Weighted norm inequalities are proved for a rough homogeneous singular integral operator and its corresponding maximal truncated singular operator. Our results are essential improvements as well as extensions of some known results on the weighted boundedness of singular integrals.
Highlights
Weighted norm inequalities are proved for a rough homogeneous singular integral operator and its corresponding maximal truncated singular operator
Throughout this paper, we let ξ denote ξ/|ξ| for ξ ∈ Rn\{0} and p denote the dual exponent to p defined by 1/ p + 1/ p = 1
Let n ≥ 2 and Sn−1 represent the unit sphere in Rn equipped with the normalized Lebesgue measure dσ = dσ(·)
Summary
Weighted norm inequalities are proved for a rough homogeneous singular integral operator and its corresponding maximal truncated singular operator. Our results are essential improvements as well as extensions of some known results on the weighted boundedness of singular integrals
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