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 | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-06-03885-2

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.