Interpolation on Convex-set Valued Lebesgue Spaces and its Applications
Functional Analysis
2024-01-02 v1
Abstract
In this paper, we obtain two interpolation theorems on convex-set valued Lebesgue spaces, which generalize the Marcinkiewicz interpolation theorem and Riesz-Thorin interpolation theorem on classical Lebesgue spaces, respectively. As applications, we obtain the boundedness of convex-set valued fractional averaging operators and fractional maximal operators, and prove the reverse factorization property of matrix weights.
Cite
@article{arxiv.2401.00398,
title = {Interpolation on Convex-set Valued Lebesgue Spaces and its Applications},
author = {Yuxun Zhang and Jiang Zhou},
journal= {arXiv preprint arXiv:2401.00398},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2210.09443 by other authors