General fractional derivatives and the Bergman projection
Journal article, 2020

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.

Besov space

Bergman projection

fractional derivative

doubling weight

Bergman space

Author

Antti Perälä

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Annales Academiae Scientiarum Fennicae Mathematica

1239-629X (ISSN)

Vol. 45 2 903-913

Subject Categories

Mathematical Analysis

DOI

10.5186/aasfm.2020.4531

More information

Latest update

2/19/2021