BOUNDEDNESS OF THE DISCRETE HILBERT TRANSFORM ON DISCRETE WEIGHTED MORREY SPACES

Rashid A. Aliev     (Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9 Bakhtiyar Vahabzade Street, Baku, AZ1141; Azerbaijan State Oil and Industry University, 20 Azadliq Avenue, Baku, AZ1010; Center for Mathematics and its Applications, Khazar University, 41 Mahsati Street, Baku, AZ1096, Azerbaijan)
Amil F. Jabiyev     (Baku State University, 23 Zahid Khalilov Street, Baku, AZ1148, Azerbaijan)

Abstract


The Hilbert transform is a multiplier operator widely used in the theory of Fourier transforms. It 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 considering discrete transforms is that experimental data are most often not obtained in a continuous manner but are 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 on these spaces.


Keywords


Discrete Hilbert transform, Morrey spaces, Weighted Morrey spaces, Discrete Morrey spaces, Discrete weighted Morrey spaces, Boundedness

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DOI: http://dx.doi.org/10.15826/umj.2026.1.002

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