A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains

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 $\Phi$-functions. It featured prominently in the monograph Orlicz Spaces and Generalized Orlicz Spaces [P. Harjulehto and P. Hästö, 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.

References in corpus (1)

• A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces

Cited by in corpus (1)

• Sufficient condition for boundedness of maximal operator on weighted generalized Orlicz spaces