Pointwise inequalities of logarithmic type in Hardy-Hölder spaces

Hardy Inequalities in Function Spaces

Reverse Hölder Inequalities and Approximation Spaces

We develop a simple geometry free context where one can formulate and prove general forms of Gehring's Lemma. We show how our result follows from a general inverse type reiteration theorem for approximation spaces. 2001 Academic Press

Hölder inequalities and sharp embeddings in function spaces of B spq and F s pq type

where in that special case c = 1 may be chosen. With exception of Subsection 1.2, all spaces in this paper are defined on R . This justifies to omit R in the sequel. One of the main aims of the paper is to study the appropriate counterparts of (1.1.1) and (1.1.2) for the spaces B pq and F s pq . That means for a given smoothness s we are looking for B p1q1 B s p2q2 ⊂ B pq (1.1.4) 1991 Mathemati...

Extremal functions for Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities

We consider a family of Caffarelli-Kohn-Nirenberg interpolation inequalities and weighted logarithmic Hardy inequalities which have been obtained recently as a limit case of the first ones. We discuss the ranges of the parameters for which the optimal constants are achieved by extremal functions. The comparison of these optimal constants with the optimal constants of Gagliardo-Nirenberg interpo...

Carleman type inequalities and Hardy type inequalities for monotone functions

This Ph.D. thesis deals with various generalizations of the inequalities by Carleman, Hardy and Pólya-Knopp. In Chapter 1 we give an introduction and overview of the area that serves as a frame for the rest of the thesis. In Chapter 2 we consider Carleman’s inequality, which may be regarded as a discrete version of Pólya-Knopp’s inequality and also as a natural limiting inequality of the discre...