Quaternionic regularity and the dibar-Neumann problem in C^2

Details Quaternionic regularity and the dibar-Neumann problem in C^2 Quaternionic regularity and the dibar-Neumann problem in C^2

2006-12-04

arxiv.org/abs/math/0612092v2

Mathematics

Complex Variables

13 pages; added references; small changes. To appear on Complex Variables and Elliptic Equations

Scientific paper

Let D be a domain in the quaternionic space H. We prove a differential criterion that characterizes Fueter-regular quaternionic functions f:bD -> H of class C^1. We find differential operators T and N, with complex coefficients, such that a function f is regular on D if and only if (N-jT)f=0 on the boundary of D (j a basic quaternion) and f is harmonic on D. As a consequence, by means of the identification of H with C^2, we obtain a non-tangential holomorphicity condition which generalizes a result of Aronov and Kytmanov. We also show how the differential criterion and regularity are related to the dibar-Neumann problem in C^2.

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