收稿日期: 2022-02-25
网络出版日期: 2022-06-30
基金资助
Supported by Natural Science Foundation of Anhui Higher Education Institutions (Grant
No. KJ2021A1050).
The Boundedness of Multilinear Commutators on Grand Variable Herz Spaces
Received date: 2022-02-25
Online published: 2022-06-30
Supported by
Supported by Natural Science Foundation of Anhui Higher Education Institutions (Grant
No. KJ2021A1050).
We consider multilinear commutators of singular integrals defined by $T_{\vec{b}}f(x) =\int_{\mathbb{R}^n}\prod^m_{i=1}(b_i(x)-b_i(y))K(x, y)f(y)dy,$
where K is a standard Calder\'{o}n-Zygmund kernel, m is a positive integer and \vec{b} b =(b1,b2,...,bm) is a family of m locally integrable functions. Based on the theory of
variable exponent and on generalization of the BMO norm, we prove the boundedness of
multilinear commutators T_{\vec{b}} on grand variable Herz spaces. The result is still new even in
the special case of m=1.
彭姗姗, 陈纪莉 . 多线性交换子在变指数Herz空间上的有界性[J]. 数学季刊, 2022 , 37(2) : 203 -213 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.009
We consider multilinear commutators of singular integrals defined by $T_{\vec{b}}f(x) =\int_{\mathbb{R}^n}\prod^m_{i=1}(b_i(x)-b_i(y))K(x, y)f(y)dy,$
where K is a standard Calder\'{o}n-Zygmund kernel, m is a positive integer and \vec{b} b =(b1,b2,...,bm) is a family of m locally integrable functions. Based on the theory of
variable exponent and on generalization of the BMO norm, we prove the boundedness of
multilinear commutators T_{\vec{b}} on grand variable Herz spaces. The result is still new even in
the special case of m=1.
Key words： Grand Herz space; Variable exponent; Multilinear commutators
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