On \(Q_p\)-spaces, relationships and their quaternionic generalization (Q2751197)

The author studies \(Q_p\)-spaces, which are defined by NEWLINE\[NEWLINEQ_p:= \Biggl\{f:f\text{ holomorphic in the unit disk \(\Delta\) and }\sup_{a\in \Delta} \int_\Delta|f'(z)|^2 g^p(z,a) dx dy< \infty\Biggr\},NEWLINE\]NEWLINE where \(g(z,a):= \ln|{1-\overline az\over a-z}|\), \(p>0\). He gives a summary of known results about imbeddings, its relations to the Bloch space, BMOA and some Besov-type spaces. Possible zero sets of functions from \(Q_p\) are described by \(p\)-Carleson measure. Then the author discusses a quaternionic extension of \(Q_p\)-spaces and corresponding properties to the holomorphic case.NEWLINENEWLINEFor the entire collection see [Zbl 0966.00026].