Restricted estimates of the fractional integral on the diagonal

被引：1
|
作者：
Chen, Ting
Sun, Wenchang [1 ,2 ]
机构：
[1] Nankai Univ, Sch Math Sci, Tianjin, Peoples R China
[2] Nankai Univ, LPMC, Tianjin, Peoples R China
来源：
MATHEMATISCHE NACHRICHTEN | 2023年 / 296卷 / 03期
基金：
中国国家自然科学基金;
关键词：
fractional integrals; mixed-norms; Riesz potentials; LEBESGUE SPACES; OPERATORS; LP;
D O I：
10.1002/mana.202000529
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For a function in a mixed-norm Lebesgue space, we study the restriction of its fractional integral on the diagonal. We show that the restriction is weakly bounded when the indices satisfy certain conditions. We give a complete characterization of such indices. To prove this result, we generalize a classical result on operators that commute with translations.
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页码：1013 / 1024
页数：12
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