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Some relations between two classes of real functions, the class of positive lower type p , denoted by Lp , and the class of positive upper type q , denoted by Uq , 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. Stević, from Hardy-Orlicz and Bergman-Orlicz type spaces to a weighted-type space are given. Mathematics subject classification (2010): 47B38, 47B33, 32A35, 32A36, 32A37.

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