L p Smoothness on Weighted Besov–Triebel–Lizorkin Spaces in terms of Sharp Maximal Functions

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

On a dual property of the maximal operator on weighted variable L^{p} spaces

where the supremum is taken over all cubes Q ⊂ R containing the point x. In [5], L. Diening proved the following remarkable result: if p− > 1, p+ < ∞ and M is bounded on Lp(·), then M is bounded on L (·), where p′(x) = p(x) p(x)−1 . Despite its apparent simplicity, the proof in [5] is rather long and involved. In this paper we extend Diening’s theorem to weighted variable Lebesgue spaces L p(·)...

Weighted Rearrangement Inequalities for Local Sharp Maximal Functions

Several weighted rearrangement inequalities for uncentered and centered local sharp functions are proved. These results are applied to obtain new weighted weak-type and strong-type estimates for singular integrals. A self-improving property of sharp function inequalities is established.

Composition operators acting on weighted Hilbert spaces of analytic functions

In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a Hilbert-Schmidt characterization and characterizes the membership in Schatten-class for these operators. Also, closed range composition operators  are investigated.