Carleson- and Hardy- type inequalities in some Banach function spaces

Abstract

Some new inequalities of Carleson- and Hardy- type in Banach function space settings are proved and discussed. In particular, these theorems both generalize and unify several classical inequalities e.g. those by Hardy, Polya-Knopp, Carleman, Hardy-Knopp, and Carleson. As applications, some new inequalities are pointed out.