Fundamental iterated convolution inequalities in weighted Lp spaces and their applications

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...

Noncommutative Lp spaces, Operator spaces and Applications

Overview of the field. NoncommutativeLp-spaces are at the heart of this conference. These spaces have a long history going back to pioneering works by von Neumann, Dixmier and Segal. They are the analogues of the classical Lebesgue spaces of pintegrable functions, where now functions are replaced by operators. These spaces have been investigated for operator algebras with a trace, and then arou...

Weighted Norm Inequalities for De Branges-rovnyak Spaces and Their Applications

Let H(b) denote the de Branges–Rovnyak space associated with a function b in the unit ball of H∞(C+). We study the boundary behavior of the derivatives of functions in H(b) and obtain weighted norm estimates of the form ‖f ‖L2(μ) ≤ C‖f‖H(b), where f ∈ H(b) and μ is a Carleson-type measure on C+ ∪ R. We provide several applications of these inequalities. We apply them to obtain embedding theorem...

Lp REGULARITY FOR CONVOLUTION OPERATOR EQUATIONS IN BANACH SPACES

Abstract. Here we utilize operator–valued Lq → Lp Fourier multiplier theorems to establish lower bound estimates for large class of elliptic integrodifferential equations in R. Moreover, we investigate separability properties of parabolic convolution operator equations that arise in heat conduction problems in materials with fading memory. Finally, we give some remarks on optimal regularity of ...

Convolution and Homogeneous Spaces