Abstract. The aim of the paper is to generalize two fundamental theorems of Boas. One of them deals with conditional integrability, another proves $p$th power integrability. Both theorems consider Fourier series with nonnegative coefficients and classical weight $x^\gamma $. The weight functions in our theorems are more general, they merely have $\beta $-power-monotone properties.

AMS Subject Classification (1991): 26D15, 40A05, 40A10, 42A32

Received January 15, 2008, and in revised form March 21, 2008. (Registered under 6032/2009.)