The ℓ <sup>s</sup>-boundedness of a family of integral operators on UMD banach function spaces

Book chapter (2019)

Authors

E. Lorist Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2019 E. Lorist
DOI: https://doi.org/10.1007/978-3-030-10850-2_20
Hardy–Littlewood maximal operator Banach function space Muckenhoupt weights UMD Integral operator ℓ-boundedness
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Published Date

2019

Language

English

Reuse Rights

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

We prove the ℓs-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 ℓs-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of ℓs-boundedness as weighted boundedness by Rubio de Francia.

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