Embeddings into Orlicz spaces via the modified Riesz potential

Abstract

We study point-wise estimates for the modified Riesz potential. We show that the point-wise estimates imply embeddings into Orlicz spaces from the L^1_p-space where the functions are defined in non-smooth domains. The Orlicz functions depend on the geometry of the domain. We show that the Orlicz function is optimal when p=1.