A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains
Functional Analysis
2025-04-04 v1
Abstract
Conditions for harmonic analysis in generalized Orlicz spaces have been studied over the past decade. One approach involves the generalized inverse of so-called weak -functions. It featured prominently in the monograph Orlicz Spaces and Generalized Orlicz Spaces [P. Harjulehto and P. H\"ast\"o, Lecture Notes in Mathematics, vol. 2236, Springer, Cham, 2019]. While generally successful, the inverse function formulation of the decay condition (A2) in the monograph contains a flaw, which we explain and correct in this note. We also present some new results related to the conditions, including a more general result for the density of smooth functions.
Keywords
Cite
@article{arxiv.2309.13331,
title = {A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains},
author = {Petteri Harjulehto and Peter Hästö and Artur Słabuszewski},
journal= {arXiv preprint arXiv:2309.13331},
year = {2025}
}