Some new inequalities for the Fourier transform for functions in generalized Lorentz spaces

A. N. Kopezhanova<sup>ab

a</sup> Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Satpayev St 2, 010008 Astana, Kazakhstan
^b Department of Engineering Sciences and Mathematics, Lulea University of Technology, SE 97187, Lulea, Sweden

Abstract: The classical Hausdorff–Young and Hardy–Littlewood–Stein inequalities, relating functions on $\mathbb{R}$ and their Fourier transforms, are extended and complemented in various ways. In particular, a variant of the Hardy–Littlewood–Stein inequality covering the case $p\geqslant2$ is proved and two-sided estimates are derived.

Keywords and phrases: Fourier transform, Hausdorff–Young's inequality, generalized Lorentz spaces, weight function, generalized monotone function.

MSC: 46E30, 42A38

Received: 25.06.2016

Language: English

Bibliographic databases:

•