Some Aspects of L-v(q) (R-d) Boolean and W-k(p,w) (R-d)

Abstract

Let 1 <= q; p < infinity and v,w be Beurling's weight functions on R-d. In this article we deal with harmonic properties of intersection space A(k,v,w)(q,p) (R-d) = L-v(q) (R-d) boolean AND W-k(p,w) (R-d) defined by aid of weighted Lebesgue space L-v(q) (R-d) and weighted Sobolev space W-k(p,w) (R-d). We research the inclusions and inequalities between the spaces A(k,v,w)(q,p) (Omega) where Omega subset of R-d be an open set. Finally, we proved that the spaces M (A(k,w)(1,p) (R-d), L-w(1) (R-d)) can be identified with the weighted spaces of bounded measures M-w (R-d).