MMN-766
Some aspects of $L_v^q({\mathbb{R}}^d)\cap W^{p,w}_k({\mathbb{R}}^d)$
Abstract
Let $1\leq p,q<\infty$ and $v,w$ be Beurlings weight functions on ${\mathbb{R}}^d$.
In this article we deal with harmonic properties of intersection space
$A^{q,p}_{k,v,w}({\mathbb{R}}^d)=L_v^q(\mathbb{R}^d)\cap W_k^{p,w}({\mathbb{R}}^d)$
defi
ned by aid of weighted Lebesgue space $L_v^q(\mathbb{R}^d)$ and weighted Sobolev space
$W_k^{p,w}({\mathbb{R}}^d)$. We research the inclusions
and inequalities between the spaces $A^{q,p}_{k,v,w}(\Omega)$, where $\Omega\subset\mathbb{R}^d$
be an open set. Finally, we investigate the space of multipliers
$M(A^{1,p}_{k,w}(\mathbb{R}^d),L_w^1(\mathbb{R}^d))$.
Vol. 16 (2015), No. 1, pp. 165-180
DOI: 10.18514/MMN.2015.766