粗糙核算子在修正Morrey空间中的有界性

The Boundedness of Rough Kernel Operators in Modified Morrey Space

令Ω∈L^(q)(S^(n-1))(1<q≤∞),并满足零度齐次条件和消失性条件,利用球壳分解研究带有粗糙核的极大算子MΩ、奇异积分算子TΩ和高维Marcinkiewicz积分算子μΩ在修正Morrey空间中的有界性。结果发现,这些算子都是从修正的Morrey空间到修正的Morrey空间有界的,其中,修正的Morrey空间是包含于Morrey空间与勒贝格空间之交。

LetΩ∈L^(q)(S^(n-1))(1<q≤∞)be homogeneous of degree zero and has mean value zero on Sn-1.Using the spherical shell decomposition,we prove that the maximal operator MΩ,the singular integral TΩand the Marcinkiewicz integral of higher dimensionμΩwith rough kernels are all bounded operators from modified Morrey space to modified Morrey space.Here the modified Morrey space is included in the intersection of Morrey space and Lebesgue space.