设Ω ∈ Lq(Sn?1)且1 < q ≤ ∞是零次齐次函数,并且它在Sn?1上的平均值为零. 本文将研究具有粗糙核的齐次奇异积分和Marcinkiewicz积分在加权Morrey空间Lp,κ(w)上的有界性,q’ ≤ p < ∞ (或者q’ < p < ∞)且0 < κ < 1.我们还将证明由BMO(Rn)函数b(x)和这些粗糙算子所生成的交换子在加权Morrey空间Lp,κ(w)上的有界性,q’ < p < ∞且0 < κ < 1.
Abstract
Let Ω ∈ Lq(Sn?1) with 1 < q ≤ ∞ be homogeneous of degree zero and has mean value zero on Sn?1. In this paper, we will study the boundedness of homogeneous singular integrals and Marcinkiewicz integrals with rough kernel on the weighted Morrey spaces Lp,κ(w) for q’ ≤ p < ∞ (or q’ < p < ∞) and 0 < κ < 1. We will also prove that the commutator operators formed by a BMO(Rn) function b(x) and these rough operators are bounded on the weighted Morrey spaces Lp,κ(w) for q’ < p < ∞ and 0 < κ < 1.
关键词
齐次奇异积分 /
Marcinkiewicz积分 /
粗糙核 /
加权Morrey空间
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Key words
homogeneous singular integrals /
Marcinkiewicz integrals /
rough kernel /
weighted Morrey spaces
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参考文献
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