The ${\ell }^s$-boundedness of a family of integral operators on UMD Banach function spaces

Abstract

We prove the ${\ell }^s$-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the ${\ell }^s$-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of ${\ell }^s$-boundedness as weighted boundedness by Rubio de Francia.

13 pages. Generalization of arXiv:1410.6657

References in corpus (2)

• Rs-sectorial operators and generalized Triebel-Lizorkin spaces
• On the R-boundedness of stochastic convolution operators

Cited by in corpus (1)

• Euclidean structures and operator theory in Banach spaces