Riesz spaces with generalized Orlicz growth
Abstract
We consider a Riesz $\phi$-variation for functions $f$ defined on the real line when $\varphi:\Omega\times[0,\infty)\to[0,\infty)$ is a generalized $\Phi$-function. We show that it generates a quasi-Banach space and derive an explicit formula for the modular when the function $f$ has bounded variation. The resulting $BV$-type energy has previously appeared in image restoration models. We generalize and improve previous results in the variable exponent and Orlicz cases and answer a question regarding the Riesz--Medvedev variation by Appell, Banaś and Merentes [\emph{Bounded Variation and Around}, Studies in Nonlinear Analysis and Applications, Vol. 17, De Gruyter, Berlin/Boston, 2014].
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2022
- DOI:
- 10.48550/arXiv.2204.14128
- arXiv:
- arXiv:2204.14128
- Bibcode:
- 2022arXiv220414128H
- Keywords:
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- Mathematics - Functional Analysis;
- 26A45;
- 26B30