We prove an equiconvergence theorem for Laguerre expansions with partial sums related to partial sums of the (non-modified) Hankel transform. Combined with an equiconvergence theorem recently proved by Colzani, Crespi, Travaglini and Vignati this gives, via the Carleson-Hunt theorem, a.e. convergence results for partial sums of Laguerre function expansions.
@article{bwmeta1.element.bwnjournal-article-smv118i3p285bwm,
author = {Krzysztof Stempak},
title = {Equiconvergence for Laguerre function series},
journal = {Studia Mathematica},
volume = {119},
year = {1996},
pages = {285-300},
zbl = {0973.42016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv118i3p285bwm}
}
Stempak, Krzysztof. Equiconvergence for Laguerre function series. Studia Mathematica, Tome 119 (1996) pp. 285-300. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv118i3p285bwm/
[00000] [CCTV] L. Colzani, A. Crespi, G. Travaglini and M. Vignati, Equiconvergence theorems for Fourier-Bessel expansions with applications to the harmonic analysis of radial functions in euclidean and noneuclidean spaces, Trans. Amer. Math. Soc. 338 (1993), 43-55. | Zbl 0785.42006
[00001] [Ma] C. Markett, Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), 19-37. | Zbl 0515.42023
[00002] [M1] B. Muckenhoupt, Mean convergence of Hermite and Laguerre series. II, Trans. Amer. Math. Soc. 147 (1970), 433-460.
[00003] [M2] B. Muckenhoupt, Equiconvergence and almost everywhere convergence of Hermite and Laguerre series, SIAM J. Math. Anal. 1 (1970), 295-321. | Zbl 0201.08501
[00004] [St1] K. Stempak, On connections between Hankel, Laguerre and Heisenberg multipliers, J. London Math. Soc. 51 (1995), 286-298. | Zbl 0824.42004
[00005] [St2] K. Stempak, Transplanting maximal inequalities between Laguerre and Hankel multipliers, Monatsh. Math., to appear. | Zbl 0866.42006
[00006] [Sz] G. Szegö, Orthogonal Polynomials, Colloq. Publ. 23, Amer. Math. Soc., New York, 1939.