On absolute matrix summability of orthogonal series

In this paper, we prove two theorems on ∣A∣k, 1 ≤ k ≤ 2, summability of orthogonal series. The first one gives a sufficient condition under which an orthogonal series is absolutely summable almost everywhere, and the second one, is a general theorem, which also gives a sufficient condition so that an orthogonal series is absolutely summable almost everywhere, but it involves a positive numerical sequence that satisfies certain additional conditions. Besides, several known and new results are deduced as corollaries of the main results. Mathematics Subject Classification: 42C15, 40F05, 40D15, 40G99