SMOOTHING PROPERTIES OF BILINEAR OPERATORS AND LEIBNIZ-TYPE RULES IN LEBESGUE AND MIXED LEBESGUE SPACES

被引：52
|
作者：
Hart, Jarod [1 ]
Torres, Rodolfo H. [2 ]
Wu, Xinfeng [2 ,3 ]
机构：
[1] Univ Kansas, Higuchi Biosci Ctr, Lawrence, KS 66047 USA
[2] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
[3] China Univ Min & Technol, Dept Math, Beijing 100083, Peoples R China
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 370卷 / 12期
关键词：
Bilinear operators; multipliers; maximal function; smoothing properties; fractional derivatives; Leibniz rule; mixed Lebesgue spaces; WEIGHTED NORM INEQUALITIES; PSEUDODIFFERENTIAL-OPERATORS; VALUED INEQUALITIES; SINGULAR-INTEGRALS; SYMBOLIC-CALCULUS; HORMANDER CLASSES; TRIEBEL-LIZORKIN; DECOMPOSITION; BMO;
D O I：
10.1090/tran/7312
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that bilinear fractional integral operators and similar multipliers are smoothing in the sense that they improve the regularity of functions. We also treat bilinear singular multiplier operators which preserve regularity and obtain several Leibniz-type rules in the context of Lebesgue and mixed Lebesgue spaces.
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页码：8581 / 8612
页数：32
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