Fourier Series and Transforms in Grand Lebesgue Spaces As an particular case - exponential Orlicz spaces

Mathematics – Functional Analysis

Scientific paper

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Scientific paper

In this article we investigate the Fourier series and transforms for the
functions defined on the [-pi, pi]^ d or on the R^d and belonging to the
(Bilateral) Grand Lebesgue Spaces. As a particular case we obtain some results
about Fourier's transform in the so-called exponential Orlicz spaces. We
construct also several examples to show the exactness of offered estimations.

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