A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces

DOI10.1007/S12220-022-01052-5arXiv2202.10878MaRDI QIDQ6391847

Peter Hästö

Publication date: 22 February 2022

Abstract: 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.

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Convex sets in topological linear spaces; Choquet theory (46A55) Inequalities and extremum problems in real or complex geometry (51M16)

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