Pitt-Type Inequalities For General Monotone Functions

Abstract

In this paper, we study Pitt-type results for the Fourier transform. A new class of general monotone functions is introduced as a subclass of BV functions, and basic properties are established. It is shown that GM(R; τ, κ) is a natural generalization of the classical general monotone functions first introduced by Liflyand and Tikhonov in 2008. Pitt’s inequality is proven for functions from this class for the range of weight parameters extending known results.