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The convergence of multidimensional fourier-bessel series

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Abstract

We study the convergence of series of eigenfunctions of the Laplacian in the unit ballB d. The problem is posed in the spacesL prad (L 2ang ). A convergence result is obtained in the sharp range2d/(d + 1) <p <2d/(d-1). There is a close connection with the spherical summation of classical trigonometric expansions. The proofs involve weighted inequalities for singular integrals, as well as a precise decomposition of oscillatory integrals using van der Corput’s method.

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Authors and Affiliations

  1. Institute of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark

    P. Balodis

  2. Depto. Matematicas, Univ. Autónoma Madrid, 28049, Madrid, Spain

    A. Córdoba

Authors
  1. P. Balodis
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  2. A. Córdoba
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Balodis, P., Córdoba, A. The convergence of multidimensional fourier-bessel series. J. Anal. Math. 77, 269–286 (1999). https://doi.org/10.1007/BF02791263

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  • DOI: https://doi.org/10.1007/BF02791263

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