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Short communications

Integrability of the Fourier transforms of $\alpha$-monotone functions

A. Mukanov

Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 2 Satpaev St., 010008 Astana, Kazakhstan

Abstract: We define a class of $\alpha$-monotone functions. We study of integrability conditions of the Fourier transforms of functions from this class.

Keywords and phrases: Fourier transform, Lorentz spaces, $\alpha$-monotone functions, fractional integral.

MSC: 42B10

Received: 10.02.2015

Language: English

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