A1 Refereed original research article in a scientific journal
A Fundamental Condition for Harmonic Analysis in Anisotropic Generalized Orlicz Spaces
Authors: Hästö Peter A.
Publisher: SPRINGER
Publication year: 2023
Journal: Journal of Geometric Analysis
Journal name in source: JOURNAL OF GEOMETRIC ANALYSIS
Journal acronym: J GEOM ANAL
Article number: 7
Volume: 33
Issue: 1
Number of pages: 15
ISSN: 1050-6926
eISSN: 1559-002X
DOI: https://doi.org/10.1007/s12220-022-01052-5
Web address : https://link.springer.com/article/10.1007/s12220-022-01052-5
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/178720987
Anisotropic generalized Orlicz spaces have been investigated in many recent papers, but the basic assumptions are not as well understood as in the isotropic case. We study the greatest convex minorant of anisotropic Phi-functions and prove the equivalence of two widely used conditions in the theory of generalized Orlicz spaces, usually called (A1) and (M). This provides a more natural and easily verifiable condition for use in the theory of anisotropic generalized Orlicz spaces for results such as Jensen's inequality which we obtain as a corollary.
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