Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (3): 771-788.doi: 10.1007/s10473-025-0302-8

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COMMUTATOR ESTIMATES FOR VECTOR FIELDS ON BESOV SPACES WITH VARIABLE SMOOTHNESS AND INTEGRABILITY

BenMahmoud SALAH   

  1. Laboratory of Functional Analysis and Geometry of Spaces, Department of Mathematics, M'sila University, M'sila 28000, Algeria; Department of Mathematics, Faculty of Science and Technology, University of Ahmed Zabana, Relizane 48000, Algeria
  • Received:2024-01-03 Revised:2024-04-27 Online:2025-05-25 Published:2025-09-30
  • About author:BenMahmoud SALAH, E-mail: salah.benmahmoud@univ-msila.dz; salah.benmahmoud@univ-relizane.dz

Abstract: In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability, and under no vanishing assumptions on the divergence of vector fields. Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fluid mechanics.

Key words: commutator, vector fields, Besov space, variable exponent

CLC Number: 

  • 46E35
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