Functions of Bounded Variation and Their Fourier Transforms, 1st ed. 2019 Applied and Numerical Harmonic Analysis Series

Functions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform.  

This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series.   

Covers almost all the aspects of the behavior of the Fourier transforms of functions of bounded variation

Many known and new spaces are considered

A must to read for those who are interested in function spaces and their interrelations