Some aspects of Lqυ (Rd)∩Wp,wk (Rd)

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,pk,υ,w (Rd) = Lqυ (Rd) ∩ Wp,wk (Rd) defined by aid of weighted Lebesgue space Lqυ (Rd) and weighted Sobolev space Wp,wk (Rd). We research the inclusions and inequalities between the spaces Aq,pk,υ,w (Ω) where Ω ⊂ Rd be an open set. Finally, we proved that the spaces M (A1,pk,w (Rd), L1w (Rd)) can be identified with the weighted spaces of bounded measures Mw (Rd).