Transferring Boundedness from Conjugate Operators Associated with Jacobi, Laguerre, and Fourier–Bessel Expansions to Conjugate Operators in the Hankel Setting |
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Authors: | Jorge J Betancor Juan C Fariña Lourdes Rodríguez-Mesa Alejandro Sanabria-García |
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Institution: | (1) Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, 38271 La Laguna, Sta. Cruz de Tenerife, Spain |
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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.
This paper is partially supported by MTM2004/05878. Third and fourth authors are also partially supported by grant PI042004/067. |
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Keywords: | Laguerre Jacobi Fourier– Bessel Conjugate Transference |
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