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Eurasian Math. J., 2017, Volume 8, Number 1, Pages 58–66 (Mi emj248)  

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

A. N. Kopezhanovaab

a 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.

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Bibliographic databases:
MSC: 46E30, 42A38
Received: 25.06.2016
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Citation: A. N. Kopezhanova, “Some new inequalities for the Fourier transform for functions in generalized Lorentz spaces”, Eurasian Math. J., 8:1 (2017), 58–66

Citation in format AMSBIB
\Bibitem{Kop17}
\by A.~N.~Kopezhanova
\paper Some new inequalities for the Fourier transform for functions in generalized Lorentz spaces
\jour Eurasian Math. J.
\yr 2017
\vol 8
\issue 1
\pages 58--66
\mathnet{http://mi.mathnet.ru/emj248}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000411744800005}


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