A Fundamental Condition for Harmonic Analysis in Anisotropic Generalized Orlicz Spaces



: Hästö Peter A.

Publisher: SPRINGER

: 2023

: Journal of Geometric Analysis

: JOURNAL OF GEOMETRIC ANALYSIS

: J GEOM ANAL

:  7

: 33

: 1

: 15

: 1050-6926

: 1559-002X

DOI: https://doi.org/10.1007/s12220-022-01052-5

: https://link.springer.com/article/10.1007/s12220-022-01052-5

: 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.

Last updated on 2024-26-11 at 19:29