Article ID Journal Published Year Pages File Type
4663726 Acta Mathematica Scientia 2014 14 Pages PDF
Abstract

Let h   be a measurable function defined on ℝ+ × ℝ+. Let Ω ∈ L(log L+)vq(Sn1−1 × Sn2−1) (1 ≤ vq ≤ 2)ℝ+ × ℝ+. Let Ω ∈ L(log L+)vq(Sn1−1 × Sn2−1) (1 ≤ vq ≤ 2) be homogeneous of degree zero and satisfy certain cancellation conditions. We show that the singular integral Tf(x1,x2) = p. v. ∬ℝn1+n2Ω(y′1,y′2)h(|y1|,|y2|)|y1|n1|y2|n2f(x1−y1,x2−y2)dy1dy2maps from Sp,qα1,α2F˙(ℝn1 × ℝn2) boundedly to itself for 1 < p, q < ∞, α1, α2 ∈ ℝ.1 < p, q < ∞, α1, α2 ∈ ℝ.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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