An interpolation theorem on Banach function 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...

Weak Interpolation in Banach Spaces

On Peano’s Theorem in Banach Spaces

We show that if X is a separable Banach space (or more generally a Banach with an infinite-dimensional separable quotient) then there is a continuous mapping f : X → X such that the autonomous differential equation x′ = f(x) has no solution at any point. In order to put our results into context, let us start by formulating the classical theorem of Peano. Theorem 1. (Peano) Let X = R, f : R×X → ...

On an atomic decomposition in Banach spaces

An atomic decomposition is considered in Banach space.  A method for constructing an atomic decomposition of Banach  space, starting with atomic decomposition of  subspaces  is presented. Some relations between them are established. The proposed method is used in the  study  of the  frame  properties of systems of eigenfunctions and associated functions of discontinuous differential operators.

An Interpolation Theorem for Sublinear Operators on 77„ Spaces

The purpose of this paper is to extend an interpolation theorem for sublinear operators on Lp spaces, obtained by Calderon and Zygmund, to similar operators acting on 77p spaces, p>0 [l]. We begin by making a few definitions. Let T be a mapping defined on a class of functions that are analytic in the interior of the unit circle \w\ <1, taking values that are measurable functions on some measure...