Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 771–783

CLOSURE OF BERGMAN AND DIRICHLET SPACES IN THE BLOCH NORM

Bin Liu and Jouni Rättyä

University of Eastern Finland, Department of Physics and Mathematics
P.O. Box 111, 80101 Joensuu, Finland; binl 'at' uef.fi

University of Eastern Finland, Department of Physics and Mathematics
P.O. Box 111, 80101 Joensuu, Finland; jouni.rattya 'at' uef.fi

Abstract. The closure of the weighted Bergman and Dirichlet spaces in the Bloch norm is described in terms of a kind of Lusin area function and natural level sets. In certain special cases simpler characterizations are also offered. The results are applied in the study of interpolating Blaschke products.

2010 Mathematics Subject Classification: Primary 30H30; Secondary 46E15.

Key words: Bergman space, Blaschke product, Bloch space, closure in Bloch space, Dirichlet space, doubling weight, Lusin area function.

Reference to this article: B. Liu and J. Rättyä: Closure of Bergman and Dirichlet spaces in the Bloch norm. Ann. Acad. Sci. Fenn. Math. 45 (2020), 771–783.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4533