Almost everywhere convergence of Laguerre series

ArticleOriginal scientific text

Title

Authors ¹, ²

Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China
Department of Mathematics, National Central University, Chung-Li, Taiwan 32054, Republic of China

Let

a \in ℤ^{+}

and

f \in L^{p} (ℝ^{+}), 1 \leq p \leq \infty

. Denote by

c_{j}

the inner product of f and the Laguerre function

ℒ^{a}_j

. We prove that if

{c_{j}}

satisfies !$!lim_{λ↓1} \overline lim_{n→∞} ∑_{n

almost everywhere convergence, Cesàro means, Laguerre polynomials, Riesz means

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