arXiv Analytics

Sign in

arXiv:1810.12833 [math.FA]AbstractReferencesReviewsResources

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

Emiel Lorist

Published 2018-10-30Version 1

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.

Comments: 13 pages. Generalization of arXiv:1410.6657
Categories: math.FA, math.CA
Subjects: 42B20, 42B25, 46E30
Related articles: Most relevant | Search more
arXiv:1007.1185 [math.FA] (Published 2010-07-07)
Criteria for the Boundedness of Potential Operators in Grand Lebesgue Spaces
arXiv:1204.2208 [math.FA] (Published 2012-04-10)
Riesz type potential operators in generalized grand Morrey spaces
arXiv:math/0612433 [math.FA] (Published 2006-12-15)
Integral operators induced by the Fock kernel

Links

Toolbox