Almost everywhere summability of Laguerre series. II
Stempak, K.
Studia Mathematica, Tome 103 (1992), p. 317-327 / Harvested from The Polish Digital Mathematics Library
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Using methods from [9] we prove the almost everywhere convergence of the Cesàro means of Laguerre series associated with the system of Laguerre functions Lna(x)=(n!/Γ(n+a+1))1/2e-x/2xa/2Lna(x), n = 0,1,2,..., a ≥ 0. The novel ingredient we add to our previous technique is the Ap weights theory. We also take the opportunity to comment and slightly improve on our results from [9].

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:215955 
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Stempak, K. Almost everywhere summability of Laguerre series. II. Studia Mathematica, Tome 103 (1992) pp. 317-327. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv103i3p317bwm/

[00000] [1] R. Askey and I. I. Hirschman, Jr., Mean summability for ultraspherical polynomials, Math. Scand. 12 (1963), 167-177. | Zbl 0132.29501

[00001] [2] A. Bonami et J.-L. Clerc, Sommes de Cesàro et multiplicateurs des développements en harmoniques sphériques, Trans. Amer. Math. Soc. 183 (1973), 223-263.

[00002] [3] J. Długosz, Almost everywhere convergence of some summability methods for Laguerre series, Studia Math. 82 (1985), 199-209. | Zbl 0574.42020

[00003] [4] C. Markett, Norm estimates for Cesàro means of Laguerre expansions, in: Approximation and Function Spaces (Proc. Conf. Gdańsk 1979), North-Holland, Amsterdam 1981, 419-435.

[00004] [5] C. Markett, Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), 19-37. | Zbl 0515.42023

[00005] [6] B. Muckenhoupt, Poisson integrals for Hermite and Laguerre expansions, Trans. Amer. Math. Soc. 139 (1969), 231-242. | Zbl 0175.12602

[00006] [7] B. Muckenhoupt, Mean convergence of Hermite and Laguerre series. II, ibid. 147 (1970), 433-460.

[00007] [8] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton 1971. | Zbl 0232.42007

[00008] [9] K. Stempak, Almost everywhere summability of Laguerre series, Studia Math. 100 (1991), 129-147. | Zbl 0731.42027

[00009] [10] S. Thangavelu, Summability of Laguerre expansions, Anal. Math. 16 (1990), 303-315. | Zbl 0737.41033