An F. and M. Riesz theorem for planar vector fields |
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| Authors: | S Berhanu J Hounie |
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| Institution: | (1) Department of Mathematics, Temple University, Philadelphia, PA 19122-6094, USA (e-mail: berhanu@euclid.math.temple.edu) , US;(2) Departamento de Matemática, UFSCar, 13.565-905, S ao Carlos, SP, Brazil (e-mail: hounie@ufscar.dm.br) , BR |
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| 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 is an open subset of the plane with smooth boundary, satisfiesLu=0 on , has tempered growth at the boundary, and its weak boundary value is a measure , then is absolutely continuous with respect to Lebesgue measure on the noncharacteristic portion of .
Received March 10, 2000 / Published online April 12, 2001 |
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| Keywords: | Mathematics Subject Classification (2000): 35F15 30E25 28A99 42A99 42B30 42A38 46F20 |
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