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An extension problem related to the fractional Branson-Gover operators

Journal article
Authors J. Frahm
B. Orsted
Genkai Zhang
Published in Journal of Functional Analysis
Volume 278
Issue 5
ISSN 0022-1236
Publication year 2020
Published at Department of Mathematical Sciences
Language en
Links dx.doi.org/10.1016/j.jfa.2019.10839...
Keywords Branson-Gover operators, Differential forms, Extension problem, Poisson, transform, Mathematics
Subject categories Mathematics

Abstract

The Branson-Gover operators are conformally invariant differential operators of even degree acting on differential forms. They can be interpolated by a holomorphic family of conformally invariant integral operators called fractional Branson-Gover operators. For Euclidean spaces we show that the fractional Branson-Gover operators can be obtained as Dirichlet-to-Neumann operators of certain conformally invariant boundary value problems, generalizing the work of Caffarelli-Silvestre for the fractional Laplacians to differential forms. The relevant boundary value problems are studied in detail and we find appropriate Sobolev type spaces in which there exist unique solutions and obtain the explicit integral kernels of the solution operators as well as some of their properties. (C) 2019 Elsevier Inc. All rights reserved.

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