Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 903–913

GENERAL FRACTIONAL DERIVATIVES AND THE BERGMAN PROJECTION

Antti Perälä

Chalmers University of Technology and the University of Gothenburg
Department of Mathematical Sciences, Gothenburg SE-412 96, Sweden; antti.perala 'at' gu.se

Abstract. In this note we study some basic properties of general fractional derivatives induced by weighted Bergman kernels. As an application we demonstrate a method for generating pre-images of analytic functions under weighted Bergman projections. This approach is useful for proving the surjectivity of weighted Bergman projections in cases when the target space is not a subspace of the domain space (such situations arise often when dealing with Bloch and Besov spaces). We also discuss a fractional Littlewood–Paley formula.

2010 Mathematics Subject Classification: Primary 32A36, 30H30, 30H25.

Key words: Bergman space, Besov space, Bergman projection, doubling weight, fractional derivative.

Reference to this article: A. Perälä: General fractional derivatives and the Bergman projection. Ann. Acad. Sci. Fenn. Math. 45 (2020), 903–913.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4531