Almost everywhere summability of Laguerre series

Krzysztof Stempak

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Almost everywhere convergence of Laguerre series

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Some remarks on the existence of a resolvent

Masanori Kishi (1975)

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Noting that a resolvent is associated with a convolution kernel $x$ satisfying the domination principle if and only if $x$ has the dominated convergence property, we give some remarks on the existence of a resolvent.

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Louis Pigno (1976)

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Almost everywhere summability of Laguerre series. II

K. Stempak (1992)

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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 $L_{n}^{a} (x) = {(n! / Γ (n + a + 1))}^{1 / 2} e^{- x / 2} x^{a / 2} L_{n}^{a} (x)$ , n = 0,1,2,..., a ≥ 0. The novel ingredient we add to our previous technique is the $A_{p}$ weights theory. We also take the opportunity to comment and slightly improve on our results from [9].