On analytic and meromorphic functions and spaces of QK-type

Starting from a nondecreasing function K : [0, infinity) --> [0, infinity), we introduce a Mobius-invariant Banach space Q(K). of functions analytic in the unit disk in the plane. We develop a general theory of these spaces, which yields new results and also, for special choices of K, gives most basic properties of Q(p)-spaces. We have found a general criterion on the kernels K-1 and K-2, K-1 less than or equal to K-2, such that Q(K2) not subset of or equal to Q(K1), as well as necessary and sufficient conditions on K so that Q(K) = B or Q(K) = D, where the Bloch space 5 and the Dirichlet space D are the largest, respectively smallest:, spaces of Q(K)-type. We also consider the meromorphic counterpart Q(K)(#) of Q(K) and discuss the differences between Q(K)-spaces and Q(K)(#)-classes