Boundedness of the discrete Hilbert transform on discrete weighted Morrey spaces

TL;DR

This paper investigates the boundedness of the discrete Hilbert transform within discrete weighted Morrey spaces, contributing to the understanding of its behavior in these function spaces relevant to digital signal processing.

Contribution

It establishes the boundedness of the discrete Hilbert transform on discrete weighted Morrey spaces, a novel result in harmonic analysis.

Findings

Discrete Hilbert transform is bounded on discrete weighted Morrey spaces.

Provides new insights into the behavior of discrete transforms in function spaces.

Enhances theoretical foundation for applications in digital signal processing.

Abstract

The Hilbert transform is a multiplier operator and is widely used in the theory of Fourier transforms. The Hilbert transform was the motivation for the development of modern harmonic analysis. Its discrete version is also widely used in many areas of science and technology and plays an important role in digital signal processing. The essential motivation behind thinking about discrete transforms is that experimental data are most often not taken in a continuous manner but sampled at discrete time values. Since much of the data collected in both the physical sciences and engineering are discrete, the discrete Hilbert transform is a rather useful tool in these areas for the general analysis of this type of data. In this paper, we discuss the discrete Hilbert transform on discrete Weighted Morrey spaces and obtain its boundedness in these spaces.