Characterizations of QT Spaces

AbstractWe introduce a new space, QT space, of analytic functions on the unit disk in terms of a nondecreasing function T. The relation between QT and Qp spaces, which have attracted considerable attention, is given by studying the growth order of T. The counterpart Q#T of QT for the meromorphic case is also considered and investigated. We note that some characterizations of Q#T and QT are different. Moreover, our results answer a question raised by P. Wu (1998, Complex Variables35, 157–170) in the negative