Boundedness of composition operators from Lorentz spaces to Orlicz spaces
Functional Analysis
2024-09-18 v3
Abstract
The boundedness (continuity) of composition operators from some function space to another one is significant, though there are few results about this problem. Thus, in this study, we provide necessary and sufficient conditions on the boundedness of composition operators from Lorentz spaces to Orlicz spaces. We also give a counter example of a mapping which implies unboundedness of the composition operators from a Lebesgue space to another Lebesgue space with . We emphasize that the measure spaces associated with the Lorentz space may be different from those associated with the Orlicz spaces. We give more examples and counterexamples of the composed mappings in the conditions satisfying our main results.
Cite
@article{arxiv.2404.18107,
title = {Boundedness of composition operators from Lorentz spaces to Orlicz spaces},
author = {Naoya Hatano and Masahiro Ikeda and Ryota Kawasumi},
journal= {arXiv preprint arXiv:2404.18107},
year = {2024}
}