English

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