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Transplantation and multiplier theorems for Fourier-Bessel expansions
Author(s):
Óscar
Ciaurri;
Krzysztof
Stempak
Journal:
Trans. Amer. Math. Soc.
358
(2006),
4441-4465.
MSC (2000):
Primary 42C10;
Secondary 44A20
Posted:
February 20, 2006
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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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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:
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
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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