Fractional Riesz Transforms and Applications on Exterior Domains

Abstract

In this paper, we investigate the boundedness of the fractional Riesz transform associated with the Dirichlet Laplacian on exterior C^1,Dini domains in ℝⁿ, n ≥ 2. We establish the boundedness of fractional Riesz transforms on these domains, which in particular covers the planar case. Some applications are also provided.

Keywords

Fractional Riesz transform / exterior domain / 42B37 / 42B20 / 35K08

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