Abstract:
The classical inequalities of Bochkarev play a very important role in harmonic analysis. The meaning of
these inequalities lies in the connection between the metric characteristics of functions and the summability
of their Fourier coefficients. One of the most important directions of harmonic analysis is the theory of
Fourier series. His interest in this direction is explained by his applications in various departments of
modern mathematics and applied sciences, as well as the availability of many unsolved problems. One
of these problems is the study of the interrelationships of the integral properties of functions and the
properties of the sum of its coefficients. The solution of these problems was dedicated to the efforts of many
mathematicians. And further research in this area are important and interesting problems and can give
new, unexpected effects. In the article we receive a two-dimensional analog of the Bochkarev type theorem
for the Fourier transform.
