带变量核奇异积分算子的ρ-变差  

ρ-Variation for Singular Integral Operators with Variable Kernels

作　　者：龚珍兵 陈艳萍[1] 陶文宇 Gong Zhenbing;Chen Yanping;Tao Wenyu(Department of Applied Mathematics,School of Mathematics and Physics,University of Science and Technology Beijing,Beijing 100083)

机构地区：[1]北京科技大学数理学院,北京100083

出　　处：《数学物理学报（A辑）》2020年第6期1446-1460,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(11871096,11471033)。

摘　　要：该文证明了带粗糙变量核Ω∈L^∞(R^n)×L^q(S^n-1)奇异积分算子的变差在L^2(R^n)上的有界性,其中q>2(n-1)/n,n≥2.此外,该文还得到了具有光滑变量核奇异积分算子的加权变差不等式并将其结果扩展到了Morrey空间.In this paper,we will prove that the variation of singular integral operators with rough variable kernels are bounded on L^2(R^n)ifΩ∈L^∞(R^n)×L^q(S^n-1)for q>2(n-1)/n,and n≥2.Moreover,we can also obtain the weighted variational inequalities for singular integral operators with smooth variable kernels.Finally,we extend the result to the Morrey spaces.

关 键 词：变差不等式 变量核 奇异积分 AP权 MORREY空间 

分 类 号：O174.2[理学—数学]