The Bochner-Riesz means for Fourier-Bessel expansions: norm inequalities for the maximal operator and almost everywhere convergence
Abstract
In this paper, we develop a thorough analysis of the boundedness properties of the maximal operator for the Bochner-Riesz means related to the Fourier-Bessel expansions. For this operator, we study weighted and unweighted inequalities in the spaces L^p((0,1),x^{2\nu+1}dx). Moreover, weak and restricted weak type inequalities are obtained for the critical values of p. As a consequence, we deduce the almost everywhere pointwise convergence of these means.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2012
- DOI:
- 10.48550/arXiv.1207.5749
- arXiv:
- arXiv:1207.5749
- Bibcode:
- 2012arXiv1207.5749C
- Keywords:
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- Mathematics - Functional Analysis
- E-Print:
- 25 pages, 2 figures