Boundedness and Compactness for the Iterated Commutators of Bilinear Fractional Maximal Operators on Weighted Morrey Spaces

Axioms 2026 Open access

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Authors: Kangmin Zhu, Zhiyu Lin, Xiangxing Tao, Chunmei Zhang
DOI: 10.3390/axioms15020131
Cited by: 0

Abstract

Let Mα be the bilinear fractional maximal operator. In this paper, we prove that the commutators Mα,bi in the i-th entry (i=1,2) and the bilinear iterated commutators Mα,b→ of Mα are bounded operators from product weighted Morrey spaces Lp1,κp1q1w1p1,w1q1×Lp2,κp2q2w2p2,w2q2 to weighted Morrey spaces Lq,κvw→q, provided that b∈BMO(Rn) and b→=(b1,b2)∈BMO(Rn)×BMO(Rn). Furthermore, by using the techniques of function decompositions and the Fréchet–Kolmogorov theorem on weighted Morrey spaces, the compactness of Mα,bi(i=1,2) and Mα,b→ are also established whenever b∈CMO(Rn) and b→=(b1,b2)∈CMO(Rn)×CMO(Rn), where CMO(Rn) denotes the closure of Cc∞(Rn) in the BMO(Rn) topology.

Fields of Study & Subjects

Advanced Harmonic Analysis Research Mathematical Analysis and Transform Methods Approximation Theory and Sequence Spaces

Publication details

Journal / source
Axioms
Volume
15
Issue
2
Pages
131–131
Publication date
11 February 2026
Language
EN