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Families of Young functions and limits of Orlicz norms
Published online by Cambridge University Press: 29 May 2023
Abstract
Given a $\sigma $-finite measure space $(X,\mu )$, a Young function $\Phi $, and a one-parameter family of Young functions $\{\Psi _q\}$, we find necessary and sufficient conditions for the associated Orlicz norms of any function $f\in L^\Phi (X,\mu )$ to satisfy
The constant C is independent of f and depends only on the family $\{\Psi _q\}$. Several examples of one-parameter families of Young functions satisfying our conditions are given, along with counterexamples when our conditions fail.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society
Footnotes
S. Rodney was supported by the NSERC Discovery Grant Program. S.F. MacDonald was supported by the NSERC USRA Program and the Department of Mathematics & Statistics at McMaster University.