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Transferring Boundedness from Conjugate Operators Associated with Jacobi, Laguerre, and Fourier–Bessel Expansions to Conjugate Operators in the Hankel Setting

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Abstract

In this paper we establish transference results showing that the boundedness of the conjugate operator associated with Hankel transforms on Lorentz spaces can be deduced from the corresponding boundedness of the conjugate operators defined on Laguerre, Jacobi, and Fourier–Bessel settings. Our result also allows us to characterize the power weights in order that conjugation associated with Laguerre, Jacobi, and Fourier–Bessel expansions define bounded operators between the corresponding weighted L p spaces.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, 38271, La Laguna, Sta. Cruz de Tenerife, Spain

    Jorge J. Betancor, Juan C. Fariña, Lourdes Rodríguez-Mesa & Alejandro Sanabria-García

Authors
  1. Jorge J. Betancor
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  2. Juan C. Fariña
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  3. Lourdes Rodríguez-Mesa
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  4. Alejandro Sanabria-García
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Corresponding author

Correspondence to Jorge J. Betancor.

Additional information

Communicated by Paul L. Butzer.

Dedicated to our friend and teacher José Rodríguez, to celebrate his 60th birthday.

This paper is partially supported by MTM2004/05878. Third and fourth authors are also partially supported by grant PI042004/067.

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Betancor, J.J., Fariña, J.C., Rodríguez-Mesa, L. et al. Transferring Boundedness from Conjugate Operators Associated with Jacobi, Laguerre, and Fourier–Bessel Expansions to Conjugate Operators in the Hankel Setting. J Fourier Anal Appl 14, 493–513 (2008). https://doi.org/10.1007/s00041-008-9025-1

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  • DOI: https://doi.org/10.1007/s00041-008-9025-1

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