A Survey of Q—Spaces and Q#-Classes
We study Q-spaces and Q #-classes which are Möbius-invariant, weighted Dirichlet spaces or classes of analytic or meromorphic functions in the unit disc in the plane. Generalizations to half-spaces in higher dimensions are also possible. In the analytic case, they are subspaces of BMOA or of the Bloch space B. In the meromorphic case, they are subclasses of the class of normal functions N or of the class of spherical Bloch functions B #. In the first part of the survey, we discuss concrete examples where different kinds of p-Carleson measures (0 < p < 1) are important. In the last section, we discuss a more general theory which gives both new results and new proofs of several results from the first part.
KeywordsMeromorphic Function Besov Space Blaschke Product Carleson Measure Dirichlet Space
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