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The Journal of Geometric Analysis

, Volume 25, Issue 2, pp 910–923 | Cite as

Quaternionic Beltrami Equations with VMO Coefficients

  • Aleksis KoskiEmail author
Article

Abstract

We use quaternions to solve a certain type of elliptic first-order partial differential equation concerning functions from \(\mathbb{R}^{4}\) to itself. This equation is, in fact, a quaternionic analogue of the general linear Beltrami equation in the plane. The methods used combine Fredholm theory and Fourier multipliers to invert certain types of operators acting on the L p spaces.

Keywords

Quaternions Beltrami equation Beurling transform 

Mathematics Subject Classification

30G35 47N20 35J46 42B20 

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Copyright information

© Mathematica Josephina, Inc. 2013

Authors and Affiliations

  1. 1.HelsinkiFinland

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