具有粗糙核的奇异积分算子及其交换子在加权(L^q,L^p)~α(R^n)空间上的有界性

Boundedness of the Singular Integral Operators with Rough Kernel and Its Commutator on Weighted (L^q, L^p)~α(R^n) Spaces

利用Ap权性质及分析中的不等式,讨论具有粗糙核的奇异积分算子TΩ及其与BMO函数b生成的交换子b,TΩ在加权共合空间(Lωq,Lp)α(Rn)上的有界性,其中1<q≤α<p≤∞.

In this paper, the nature of Ap weight and H？lder inequality were used to discuss the boundedness of singular integral operator with rough kernel and its commutator with a BMO （ R^n） function b （x） on the weighted （Lω^q , L^p ）^α（R^n ） spaces, where there was 1＆lt;q≤α＆lt;p≤∞.