Almost everywhere convergence of some summabillity methods for Laguerre series

Jolanta Długosz

Displaying similar documents to “Almost everywhere convergence of some summabillity methods for Laguerre series”

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].

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Almost everywhere convergence of Laguerre series

Chang-Pao Chen, Chin-Cheng Lin (1994)

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Equisummability Theorems for Laguerre Series

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Here we prove results about Riesz summability of classical Laguerre series, locally uniformly or on the Lebesgue set of the function f such that (∫(1 + x)^(mp) |f(x)|^p dx )^(1/p) < ∞, for some p and m satisfying 1 ≤ p ≤ ∞, −∞ < m < ∞.

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Biesterfeldt, H.J. jr. (1966)

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Z. Ciesielski (1963)

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H. König, D. Lewis, P.-K. Lin (1983)

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Jerzy Sawa (1985)

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Annamaria Montanari, Daniele Morbidelli (2004)

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We provide a structure theorem for Carnot-Carathéodory balls defined by a family of Lipschitz continuous vector fields. From this result a proof of Poincaré inequality follows.