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具有Muckenhoupt基的乘积空间上的混合加权不等式
陈伟¹, 朱春香¹, 张超²
1.扬州大学数学科学学院, 江苏扬州 225002;2.浙江工商大学统计与数学学院, 浙江杭州 310018

摘要:

本文研究了在具有Muckenhoupt基的乘积空间上混合加权问题.利用外插函数族和Minkowski不等式获得了混合加权不等式.根据数学归纳法，可以得到混合加权不等式的一般形式.

关键词: 混合范数Lebesgue空间 Muckenhoupt基外插

DOI：

分类号:O174.2

基金项目:The first author was supported by the National Natural Science Foundation of China (11771379); the Natural Science Foundation of Jiangsu Province (BK20161326); the School Foundation of Yangzhou University (2016CXJ001). The third author was supported by the National Natural Science Foundation of China (11401525); the Natural Science Foundation of Zhejiang Province (LY18A010006).

WEIGHTED MIXED INEQUALITIES ON PRODUCT SPACES WITH MUCKENHOUPT BASES

CHEN Wei¹, ZHU Chun-xiang¹, ZHANG Chao²

1.School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China;2.School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Abstract:

We study weighted mixed inequalities on product spaces with different Muckenhoupt bases. Our approaches are mainly based on the abstract formalism of families of extrapolation pairs and Minkowski's integral inequality. Moreover, we can deduce the general case of our results by induction.

Key words: mixed norm Lebesgue space Muckenhoupt basis extrapolation