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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
Posted:
February 20, 2006
MathSciNet review:
2231384
Full-text PDF Free Access
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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.
References
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J. J. Betancor and K. Stempak, Relating multipliers and transplantation for Fourier-Bessel expansions and Hankel transform, Tohoku Math. J., 53 (2001), 109-129. MR 1808644 (2002b:42035)
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N. N. Lebedev, Special functions and its applications, Dover, New York, 1972. MR 0350075 (50:2568)
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K. Stempak, On connections between Hankel, Laguerre and Jacobi transplantation, Tohoku Math. J., 54 (2002), 471-493. MR 1936265 (2003h:42045)
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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 Wroclawska, Wyb. Wyspianskiego 27, 50-370 Wroclaw, 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
Posted:
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 after
28 years from publication.
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