Multidimensional Fourier transforms on an amalgam type space

E. Liflyand<sup>ab

a</sup> Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel
^b S.M. Nikol'skii Mathematical Institute, RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russia

Abstract: Generalizing the known results on the Fourier transforms on an amalgam type space, we introduce a multidimensional analogue of such a space, a subspace of $L^1(\mathbb{R}_+^n)$. Integrability results for the Fourier transforms are obtained provided that certain derivatives of the transformed function are in that space. As an application, we obtain conditions for the integrability of multiple trigonometric series.

Keywords and phrases: amalgam space, Fourier transform, integrability, bounded variation, Young inequality, trigonometric series.

MSC: 42B10, 42B35

Received: 02.02.2019

Language: English

DOI: 10.32523/2077-9879-2019-10-4-63-74

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