On the Representation of Functions as Fourier Integrals

Yu. S. Kolomoitsev<sup>ab

a</sup> Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
^b Donetsk National University

Abstract: Sufficient conditions for the representation of functions as the Fourier integral in $\mathbb R^d$ of a function belonging to the space $L_1\cap L_p$, where $0<p<2$, are obtained. The sharpness of these conditions is shown.

Keywords: Fourier integral, Euclidean space $\mathbb R^d$, the space $L_p$, $0<p<2$.

UDC: 517.5

Received: 23.03.2011

DOI: 10.4213/mzm9093

 English version: Mathematical Notes, 2013, 93:4, 561–570

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