Some Recent Results on Hardy Type Operators in Weighted Function Spaces and Related Topics

Abstract

What follows is a survey of recent results in several areas of the theory of function spaces which have been intensively studied in last years. In particular, we concentrate on the boundedness and compactness of the Hardy and imbedding operators and on the Poincare and Friedrichs inequalities in weighted spaces, taking the general setting of Banach function spaces as a common framework. We do not attempt to present an exhaustive survey of the topics. Our aim is to show the current state of the subjects in question with an emphasis on our contribution to their solution.