Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 621-626

DUALITY OF WEIGHTED BERGMAN SPACES WITH SMALL EXPONENTS

Antti Perälä and Jouni Rättyä

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

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

Abstract. It is shown that for each radial doubling weight ω and 0 < p < 1, the dual of the weighted Bergman space A_ω^p can be identified with the Bloch space under the A_W²-pairing, where W satisfies a two sided doubling property and depends on both ω and p. This result generalizes the duality relation (A_α^p)^∗ ≅ B, studied by Shapiro, Coifman, Rochberg and Zhu, concerning the classical weighted Bergman spaces.

2010 Mathematics Subject Classification: Primary 30H20; Secondary 46A16.

Key words: Bergman projection, Bergman space, Bloch space, Carleson measure, doubling weight, duality, reproducing kernel estimate.

Reference to this article: A. Perälä and J. Rättyä: Duality of weighted Bergman spaces with small exponents. Ann. Acad. Sci. Fenn. Math. 42 (2017), 621-626.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4239