Banach function spaces and interpolation methods III. Hausdorff-Young estimates

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...

Weak Interpolation in Banach Spaces

Interpolation between Hilbert , Banach and Operator spaces

Motivated by a question of Vincent Lafforgue, we study the Banach spaces X satisfying the following property: there is a function ε → ∆ X (ε) tending to zero with ε > 0 such that every operator T : L 2 → L 2 with T ≤ ε that is simultaneously contractive (i.e. of norm ≤ 1) on L 1 and on L ∞ must be of norm ≤ ∆ X (ε) on L 2 (X). We show that ∆ X (ε) ∈ O(ε α) for some α > 0 iff X is isomorphic to ...

Function spaces and Hausdorff dimension on fractals

We start by surveying a possible approach for function spaces of Besov type on special closed subsets of Rn. Afterwards we recall that, in the case of Sobolev spaces and Besov spaces on Rn, the Hausdorff dimension for the graphs of continuous functions belonging to such spaces has been studied by several authors, and that in the case of Besov spaces the final answer concerning the maximal possi...

Optimization Methods in Banach Spaces

In this chapter we present a selection of important algorithms for optimization problems with partial differential equations. The development and analysis of these methods is carried out in a Banach space setting. We begin by introducing a general framework for achieving global convergence. Then, several variants of generalized Newton methods are derived and analyzed. In particular, necessary a...