变量核奇异积分和分数次微分加权范不等式

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变量核奇异积分和分数次微分加权范不等式杨沿奇, 陶双平西北师范大学数学与统计学院兰州 730070 Weighted Norm Inequalities of Variable Singular Integrals and Fractional Differentiation Yan Qi YANG, Shuang Ping TAOCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, P. R. China

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摘要用T和D^γ（0 ≤ γ ≤ 1）分别表示变量核奇异积分和分数次微分算子.T^*和T^#分别为T的共轭算子及拟共轭算子.利用球调和多项式展式，本文得到了TD^γ-D^γT和（T^*-T^#）D^γ在?^q，λ_ω（Rⁿ）上的有界性.同时也得到了变量核奇异积分的积T₁T₂和拟积T₁°T₂的加权范不等式.

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收稿日期: 2019-04-10

MR (2010):

O174.2

基金资助:国家自然科学基金资助项目（11561062）

通讯作者:陶双平E-mail: taosp@nwnu.edu.cn

作者简介: 杨沿奇,E-mail:yangyanqi521@126.com

引用本文:

杨沿奇, 陶双平. 变量核奇异积分和分数次微分加权范不等式[J]. 数学学报, 2020, 63(4): 381-396. Yan Qi YANG, Shuang Ping TAO. Weighted Norm Inequalities of Variable Singular Integrals and Fractional Differentiation. Acta Mathematica Sinica, Chinese Series, 2020, 63(4): 381-396.

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