Weighted Inequalities Involving ρ-quasiconcave Operators

Some problems in mathematical analysis (e.g., in theory of function spaces, in approximation theory or in interpolation theory) lead to the investigation of weighted inequalities on certain classes of quasiconcave functions on the interval I=(a,b) ∊ R. In this book we analyse the class Qρ(I) of ρ-quasiconcave functions in a complete generality in order to establish results needed for a comprehensive study of weighted inequalities on the class Qρ(I). We illustrate our results on weighted inequalities of Hardy type, on weighted inequalities of Hardy type involving supremum, and on reverse forms of these inequalities.
Sample Chapter(s)
Chapter 1: Preliminaries

Contents:AcknowledgementPrefaceBasic NotationPreliminariesThe Set Qρ(I) and Its Propertiesρ-Discretizing SequencesDiscretization of Weighted Quasi-NormsWeighted Inequalities for ρ-Quasiconcave OperatorsBibliographyIndex
Readership: Graduate students and researchers in mathematical analysis.
ρ-quasiconcave Functions and Operators;Weighted Inequalities;Discretization;Antidiscretization0Key Features:There is no book in which weighted inequalities are studied on a general set of quasiconcave functions. Only some particular results can be found in mathematical papers. In the existing books weighted inequalities are investigated either on classes of positive measurable functions or on classes of monotone functions