Relations between two classes of real functions and applications to boundedness and compactness of operators between analytic function spaces

Some relations between two classes of real functions, the class of positive lower type p, denoted by ℓ p , and the class of positive upper type q, denoted by ���� q , which naturally appear in the definition of some Hardy-Orlicz and Bergman-Orlicz type spaces, are given. Some applications in characterizing the boundedness and compactness of an integral-Type operator introduced by S. Stevíc, from Hardy-Orlicz and Bergman-Orlicz type spaces to a weighted-Type space are given.