Some Aspects of Lqυ (Rd)∩wp,wk (Rd)

Abstract

Let 1≤q, p < ∞ and υ,w be Beurling's weight functions on Rd. In this article we deal with harmonic properties of intersection space Aq,p<inf>k,υ,w</inf> (Rd) = Lq<inf>υ</inf> (Rd) ∩ Wp,w<inf>k</inf> (Rd) defined by aid of weighted Lebesgue space Lq<inf>υ</inf> (Rd) and weighted Sobolev space Wp,w<inf>k</inf> (Rd). We research the inclusions and inequalities between the spaces Aq,p<inf>k,υ,w</inf> (Ω) where Ω ⊂ Rd be an open set. Finally, we proved that the spaces M (A1,p<inf>k,w</inf> (Rd), L1<inf>w</inf> (Rd)) can be identified with the weighted spaces of bounded measures M<inf>w</inf> (Rd). © 2015 Miskolc University Press.