Tohoku Mathematical Journal

Riesz transform characterization of Hardy spaces associated with certain Laguerre expansions

Jorge Betancor, Jacek Dziubański, and Gustavo Garrigós

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In this paper we prove Riesz transform characterizations for Hardy spaces associated with certain systems of Laguerre functions.

Article information

Tohoku Math. J. (2), Volume 62, Number 2 (2010), 215-231.

First available in Project Euclid: 23 June 2010

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Zentralblatt MATH identifier

Primary: 42B30: $H^p$-spaces
Secondary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

Hardy space Laguerre system Riesz transform


Betancor, Jorge; Dziubański, Jacek; Garrigós, Gustavo. Riesz transform characterization of Hardy spaces associated with certain Laguerre expansions. Tohoku Math. J. (2) 62 (2010), no. 2, 215--231. doi:10.2748/tmj/1277298646.

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  • J. J. Betancor, J. C. Fariña, L. Rodríguez-Mesa, A. Sanabria and J. L. Torrea, Transference between Laguerre and Hermite settings, J. Funct. Anal. 254 (2008), 826--850.
  • J. Dziubański, A note on Schrödinger operators with polynomial potentials, Colloq. Math. 78 (1998), 149--161.
  • J. Dziubański, Hardy spaces for Laguerre expansions, Constr. Approx. 27 (2008), 269--287.
  • J. Dziubański and J. Zienkiewicz, Hardy spaces associated with some Schrödinger operators, Studia Math. 126 (2) (1997), 149--160.
  • D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979), 27--42.
  • E. Harboure, J. L. Torrea and B. Viviani, Riesz transforms for Laguerre expansions, Indiana Univ. Math. J. 55 (2006), 999--1014.
  • A. Nowak and K. Stempak, Riesz transforms and conjugacy for Laguerre function expansions of Hermite type, J. Funct. Anal. 244 (2007), 399--443.
  • K. Stempak and J. L. Torrea, Poisson integrals and Riesz transforms for Hermite function expansions with weights, J. Funct. Anal. 202 (2003), 443--472.
  • S. Thangavelu, Riesz transforms and wave equation for the Hermite operator, Comm. Partial Differential Equations 15(8) (1990), 1199--1215.
  • S. Thangavelu, Lectures on Hermite and Laguerre expansions, Mathematical Notes, 42, Princeton University Press, Princeton, NJ, 1993.
  • J. Zhong, Harmonic analysis for some Schrödinger operators, Ph. D. Thesis, Princeton Univ., 1993.