A Note on Embedding Inequalities for Weighted Sobolev and Besov Spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

A Note on Integral Inequalities and Embeddings of Besov Spaces

It is shown that certain known integral inequalities imply directly a well-known embedding theorem of Besov spaces.

Interpolation Inequalities in Weighted Sobolev Spaces

In this paper we prove some interpolation inequalities between functions and their derivatives in the class of weighted Sobolev spaces defined on unbounded open subset Ω ⊂ Rn .

A Note on Weighted Composition Operators on L^p-Spaces

Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains

Extending recent work for the linear Poisson problem for the Laplacian in the framework of Sobolev-Besov spaces on Lipschitz domains by Jerison and Kenig [16], Fabes, Mendez and Mitrea [9], and Mitrea and Taylor [30], here we take up the task of developing a similar sharp theory for semilinear problems of the type ∆u − N(x, u) = F (x), equipped with Dirichlet and Neumann boundary conditions.