Holomorphic spaces in the unit disk based on Lorentz spaces on a unit circle
by
Romi Shamoyan
Bryansk State University, Russia

With the help of Lorentz spaces on the unit circle we introduce and study several new scales of functions holomorphic in the unit disk.These new classes extend classical Hardy,Bergman and Bloch spaces.We prove several sharp embedding theorems for such spaces, theorems on strong factorization of tent spaces based on Lorentz classes. New sharp assertions concerning diagonal map and representations of functionals will be also presented.We use characterizations of P- Carleson measures via Luzin area operator.Practically all results were known previously for particular values of parametrs.

References.Shamoyan R.F.Holomorphic spaces in the unit disk based on Lorentz classes on the unit circle,Izdatelstvo Ladomir,Kaluga,2008,March,75 pages,(Russian)

Date received: May 18, 2008