Multipliers for Hardy-Orlicz spaces and applications

Abstract

Using real-variable methods, we characterise multipliers for general classes of Hardy--Orlicz spaces, unifying and extending several classical results due to Hardy and Littlewood; Duren and Shields; Paley; and others. Applications of our results include inequalities involving Fourier coefficients and Fourier transforms of elements of Hardy--Orlicz spaces and their duals, as well as embeddings into spaces of generalised smoothness, Sobolev type-embeddings and Paley-Wiener type theorems.