Generalized absolute riesz summability of orthogonal series

Abstract

In this paper, for 1 ≤ k ≤ 2 and a sequence γ:={γ(n)}n=1∞ that is quasi β-power monotone decreasing with β>1−1k, we prove the |A, γ|k summability of an orthogonal series, where A is Riesz matrix. For β>12, 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.