2024/04/28 by Naoya Hatano, Masahiro Ikeda, Hatano, Naoya +3
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2404.18107
openalex publication_date 2024/04/28 · openalex created_date 2024/05/02 · openalex updated_date 2026/07/28
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 Lp to another Lebesgue space Lq with p>q. 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.