Geodesic
Almost everywhere summability of Laguerre series
Studia Mathematica, Tome 100 (1991) no. 2, pp. 129-147

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We apply a construction of generalized twisted convolution to investigate almost everywhere summability of expansions with respect to the orthonormal system of functions $ℓ_n^a(x) = (n!/Γ(n+a+1))^{1/2} e^{-x/2} L_n^a(x)$, n = 0,1,2,..., in $L^2(ℝ_+, x^adx)$, a ≥ 0. We prove that the Cesàro means of order δ > a + 2/3 of any function $f ∈ L^p(x^adx)$, 1 ≤ p ≤ ∞, converge to f a.e. The main tool we use is a Hardy-Littlewood type maximal operator associated with a generalized Euclidean convolution.
DOI : 10.4064/sm-100-2-129-147
Keywords: Laguerre expansions, generalized twisted convolution, Riesz, Cesàro and Abel-Poisson means

Krzysztof Stempak 1

1 
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Krzysztof Stempak. Almost everywhere summability of Laguerre series. Studia Mathematica, Tome 100 (1991) no. 2, pp. 129-147. doi: 10.4064/sm-100-2-129-147

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