Multidimensional Fourier transforms on an amalgam type space. (English) Zbl 1463.42018
Summary: 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.
MSC:
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 42B35 | Function spaces arising in harmonic analysis |
Keywords:
amalgam space; Fourier transform; integrability; bounded variation; Young inequality; trigonometric seriesReferences:
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