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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Transplantation and multiplier theorems for Fourier-Bessel expansions


Authors: Óscar Ciaurri and Krzysztof Stempak
Journal: Trans. Amer. Math. Soc. 358 (2006), 4441-4465
MSC (2000): Primary 42C10; Secondary 44A20
Published electronically: February 20, 2006
MathSciNet review: 2231384
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Abstract: Proved are weighted transplantation inequalities for Fourier-Bessel expansions. These extend known results on this subject by considering the largest possible range of parameters, allowing more weights and admitting a shift. The results are then used to produce a fairly general multiplier theorem with power weights for considered expansions. Also fractional integral results and conjugate function norm inequalities for these expansions are proved.


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Additional Information

Óscar Ciaurri
Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa s/n, 26004 Logroño, Spain
Email: oscar.ciaurri@dmc.unirioja.es

Krzysztof Stempak
Affiliation: Instytut Matematyki i Informatyki, Politechnika Wrocławska, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
Email: stempak@pwr.wroc.pl

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03885-2
PII: S 0002-9947(06)03885-2
Keywords: Fourier-Bessel expansions, transplantation, multipliers, weighted norm inequalities, fractional integrals
Received by editor(s): February 16, 2004
Received by editor(s) in revised form: August 24, 2004
Published electronically: February 20, 2006
Additional Notes: The research of the first author was supported by grant BFM2003-06335-603-03 of the DGI
The research of the second author was supported by KBN grant #2 P03A 028 25
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.