A note on weighted Sobolev algebras L1?(?d) ? Wpk (?d)

Abstract

Let 1 ? p < ? and ? be Beurling's weight function on ?d. In this article, we demonstrate some harmonic properties of Sobolev space Wpk (?d) which consists of all functions on ?d whose weak derivatives up to and including order k belong to Lp(?d). Also, we deal with some harmonic properties of intersection space Apk,?(?d) = L1?(?d) ? Wpk (?d) by aid of Beurling algebra L1?(?d) and Sobolev space Wpk (?d). Finally, we research the inclusions and continuous embeddings between the spaces Apk,?(?) where ? ? ?d be open set. © 2015 Ramanujan Mathematical Society.