Weighted Inequalities Involving ρ-quasiconcave Operators
Weighted Inequalities Involving ρ-quasiconcave Operators
by William Desmond Evans, Amiran Gogatishvili
English | 2018 | ISBN: 981323962X | 157 Pages | PDF | 2.72 MB
by William Desmond Evans, Amiran Gogatishvili
English | 2018 | ISBN: 981323962X | 157 Pages | PDF | 2.72 MB
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.
Contents:
Acknowledgement
Preface
Basic Notation
Preliminaries
The Set Qρ(I) and Its Properties
ρ-Discretizing Sequences
Discretization of Weighted Quasi-Norms
Weighted Inequalities for ρ-Quasiconcave Operators
Bibliography
Index
Readership: Graduate students and researchers in mathematical analysis.