Locally solvable vector fields and Hardy spaces |
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Authors: | G. Hoepfner |
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Affiliation: | a Department of Mathematics, Temple University, Philadelphia, PA 19122-6094, USA b Departamento de Matemática, UFSCar, 13.565-905, São Carlos, SP, Brazil |
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Abstract: | We characterize the boundary value of homegeneous solutions of planar one-sided locally solvable vector fields with analytic coefficients with the property that the Lp norm of their traces is locally uniformly bounded, 0<p?1. For p≠1/n, , the boundary value must locally belong to the local Hardy space hp(R) of Goldberg while for p=1/n, , the answer calls for a new class of atomic Hardy spaces if the vector field is of infinite type at some boundary point. |
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Keywords: | Locally integrable vector fields Hardy spaces Weak boundary values |
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