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Fourier transforms on an amalgam type space

We introduce an amalgam type space, a subspace of $L^1(\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the integrability of trigonometric series.

preprint2012arXivOpen access
E. Liflyand
math.CA
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