Weighted Hardy-type inequalities on the cones of monotone and quasi-concave functions

Abstract: This PhD thesis deals with weighted Hardy-type inequalities restricted to cones of monotone functions and quasi-monotone functions.The thesis consists of four papers (papers A, B, C and D) and an introduction, which gives an overview of this specific field of functional analysis and also serves to put these papers into a more general frame. The papers A and B are devoted to characterizing some weighted Hardy-type inequalities on the cones of monotone functions, while in the papers C and D we solve the similar problems for the cones of quasi-concave and $\psi-$quasi-concave functions.In paper A some two-sided inequalities for Hardy operators on the cones of monotone functions are proved for the full range of parameter $1