On the Fourier transform of functions from a Lorentz space L2,r with a mixed metric
Аралас метрикалы L2̄,r̄ Лоренц кеңiстiгiндегi Фурье функцияларының түрлендiрулерi жайлы
О преобразовании Фурье функций в пространстве Лоренца L2̄,r̄ со смешанной метрикой
Tleukhanova N.T. Mussabayeva G.K. Manarbek M.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#111Issue 3138 - 151 pp.
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.
Bochkarev’s theorem , Cauchy-Bunyakovsky inequality , Hausdorff-Young-Riesz theorem , Helder’s inequality , Lorentz Space
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L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
L.N. Gumilyov Eurasian National University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026