General fractional derivatives and the Bergman projection
Complex Variables
2018-10-05 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1810.02070,
title = {General fractional derivatives and the Bergman projection},
author = {Antti Perälä},
journal= {arXiv preprint arXiv:1810.02070},
year = {2018}
}
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12 pages