Generalized Absolute Riesz Summability of Orthogonal Series

摘要

In this paper, for 1 ≤ k ≤ 2 and a sequence γ: = {γ(n)}_(n=1)~∞ that is quasi β-power monotone decreasing with β > 1 - 1/k, we prove the |A, γ|k summability of an orthogonal series, where A is Riesz matrix. For β > 1/2, we give a necessary and sufficient condition for |A, γ|k summability, where A is Riesz matrix. Our result generalizes the result of Moricz (Acta Sci Math 23:92-95,1962) for absolute Riesz summability of an orthogonal series.