A NEW GENERALIZATION OF BOAS THEOREM FOR SOME LORENTZ SPACES Lambda(q)(omega)

Let Lambda(q)(omega), q > 0, denote the Lorentz space equipped with the (quasi) norm parallel to f parallel to(Lambda q(omega)) := (integral(1)(0) (f*(t)omega(t))(q)dt/t)(1/q) for a function integral on [0,1] and with omega positive and equipped with some additional growth properties. A generalization of Boas theorem in the form of a two-sided inequality is obtained in the case of both general regular system Phi = {phi(k)}(k=1)(infinity) and generalized Lorentz Lambda(q) (omega) spaces.