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

2010/10/20 by Eugeny Ostrovsky, Ostrovsky, E., L. Sirota +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Banach Space Theory #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1010.4305

Abstract

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.

Citations

• Nikol'skii-type inequalities for rearrangement invariant spaces
• Bide - Side Exponential and Moment Inequalities for Tails of Distributions of Polynomial Martingales

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