In the present note we obtain a generalization of certain results of Woyczyniski [7] concerning equivalence of some statements pertaining to integrability of power series. 1. A nondecreasing continuous real valued function (D defined on the nonnegative half line and vanishing only at the origin will be called an Orlicz function. Function (D E OF is said to satisfy A,, (?t>O) condition for large u if there are constants c>O and u0>0 such that (ocu)?cFD(u), u>uo. A convex Orlicz function 4) satisfying the conditions (D(U) (~~~~1'(u) lim = 0 and lim =ox u-O u u-oo U is called a Young function (YF). Function (D belongs to YF iff it admits a representation 4)(u) +(t) dt, where +(t), t>O, is positive, f(0)=O, continuous on the right, nondecreasing and limt, f+(t)= xo. We denote by M the class of Orlicz functions (D which satisfy the following condition of Mulholland [3]. There exist a convex function A, A> 1 and 0 O, an+l O [5]. Let L,,(X, ,), where 'D E zA, be the Orlicz space, i.e. the set of all complex valued measurable functions f on a measure space (X, ,u) such that the modular Sx (D(jf(x)i) dy is finite. In this paper the Hardy-Orlicz space H,0 is meant simply to be a closed subset of L,((O, 27T), cdx) spanned over trigonometric polynomials of the form N f (t) = aneft. Received by the editors March 8, 1973. AMS (MOS) subject classifications (1970). Primary 42A32; Secondary 42A1 6.