An F. and M. Riesz theorem for planar vector fields

2001/09/07 by S. Berhanu, J. Hounie
Mathematics · #math.CV

paper · pdf

published as Math. Ann. 320 (2001), 463-485 · 20 pages

arxiv created 2001/09/07 · arxiv updated 2009/11/30

Abstract

We prove that solutions of the homogeneous equation Lu=0, where L is a locally integrable vector field with smooth coefficients in two variables possess the F. and M. Riesz property. That is, if Ω is an open subset of the plane with smooth boundary, u∈ C¹(Ω) satisfies Lu=0 on Ω, has tempered growth at the boundary, and its weak boundary value is a measure μ, then μ is absolutely continuous with respect to Lebesgue measure on the noncharacteristic portion of ∂Ω.

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