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The weighted Stieltjes inequality and applications

✍ Scribed by Amiran Gogatishvili; Alois Kufner; Lars-Erik Persson

Publisher
John Wiley and Sons
Year
2012
Tongue
English
Weight
145 KB
Volume
286
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let 1 < p ≀ q < ∞. Inspired by some results concerning characterization of weighted Hardy type inequalities, where the equivalence of four scales of integral conditions was proved, we use related ideas to find some new equivalent scales of integral conditions related to the Stieltjes transform. By applying our result to weighted inequalities for the Stieltjes transform we obtain four new scales of conditions for characterization of this inequality. We also derive a new characterization for the solvability of a Riccati type equation and show via our new results that this characterization can be done in infinite many ways via our four scales of equivalent conditions.

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