The class Bp for weighted generalized Fourier transform inequalities

TL;DR

This paper establishes weighted inequalities for the Dunkl transform, a generalization of the Fourier transform, using weights from the Bp class, and applies these results to derive Pitt's inequality for power weights.

Contribution

It extends weighted inequality results to the Dunkl transform and derives Pitt's inequality for power weights, broadening the scope of Fourier analysis techniques.

Findings

Weighted inequalities for the Dunkl transform with Bp weights proved.

Application of results to Pitt's inequality for power weights.

Generalization of Fourier transform inequalities to Dunkl transform.

Abstract

In the present paper, we prove for the Dunkl transform which generalizes the Fourier transform, weighted inequalities when the weights belong to the well known class Bp. As application, we obtain for power weights Pitt's inequality.