Transplantation and multiplier theorems for Fourier-Bessel expansions
HTML articles powered by AMS MathViewer
- by Óscar Ciaurri and Krzysztof Stempak PDF
- Trans. Amer. Math. Soc. 358 (2006), 4441-4465 Request permission
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
- Jorge J. Betancor and Krzysztof Stempak, Relating multipliers and transplantation for Fourier-Bessel expansions and Hankel transform, Tohoku Math. J. (2) 53 (2001), no. 1, 109–129. MR 1808644, DOI 10.2748/tmj/1178207534
- John E. Gilbert, Maximal theorems for some orthogonal series. I, Trans. Amer. Math. Soc. 145 (1969), 495–515. MR 252941, DOI 10.1090/S0002-9947-1969-0252941-3
- J. J. Guadalupe, M. Pérez, F. J. Ruiz, and J. L. Varona, Two notes on convergence and divergence a.e. of Fourier series with respect to some orthogonal systems, Proc. Amer. Math. Soc. 116 (1992), no. 2, 457–464. MR 1096211, DOI 10.1090/S0002-9939-1992-1096211-0
- N. N. Lebedev, Special functions and their applications, Dover Publications, Inc., New York, 1972. Revised edition, translated from the Russian and edited by Richard A. Silverman; Unabridged and corrected republication. MR 0350075
- Benjamin Muckenhoupt, Transplantation theorems and multiplier theorems for Jacobi series, Mem. Amer. Math. Soc. 64 (1986), no. 356, iv+86. MR 858466, DOI 10.1090/memo/0356
- Benjamin Muckenhoupt, Richard L. Wheeden, and Wo-Sang Young, Sufficiency conditions for $L^p$-multipliers with power weights, Trans. Amer. Math. Soc. 300 (1987), no. 2, 433–461. MR 876461, DOI 10.1090/S0002-9947-1987-0876461-9
- B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17–92. MR 199636, DOI 10.1090/S0002-9947-1965-0199636-9
- Krzysztof Stempak, On connections between Hankel, Laguerre and Jacobi transplantations, Tohoku Math. J. (2) 54 (2002), no. 4, 471–493. MR 1936265
- G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
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
- 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 - © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 4441-4465
- MSC (2000): Primary 42C10; Secondary 44A20
- DOI: https://doi.org/10.1090/S0002-9947-06-03885-2
- MathSciNet review: 2231384