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Almost everywhere summability of Laguerre series

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Stempak K.

Studia Mathematica

1991

tom 100

nr 2

129-147

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.

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1 Studia Mathematica

1 Stempak K.

1 1991

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Almost everywhere summability of Laguerre series