Characterizations of Q Spaces

We 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 Qpspaces, which have attracted considerable attention, is given by studying the growth order of T. The counterpart QT of QT for the meromorphic case is also considered and investigated. We note that some characterizations of QT and QT are different. Moreover, our results answer a question raised by P. Wu Ž1998, Complex Variables 35, 157 170. in the negative