Locally solvable vector fields and Hardy spaces

We characterize the boundary value of homegeneous solutions of planar one-sided locally solvable vector fields with analytic coefficients with the property that the L p norm of their traces is locally uniformly bounded, 0 < p ⩽ 1 . For p ≠ 1 / n , n = 1 , 2 , … , the boundary value must locally b...

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Bibliographic Details
Published inJournal of functional analysis Vol. 247; no. 2; pp. 378 - 416
Main Authors Hoepfner, G., Hounie, J.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.06.2007
Subjects
Hardy spaces
Locally integrable vector fields
Weak boundary values
Weak boundary values
Locally integrable vector fields
Hardy spaces
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Summary:We characterize the boundary value of homegeneous solutions of planar one-sided locally solvable vector fields with analytic coefficients with the property that the L p norm of their traces is locally uniformly bounded, 0 < p ⩽ 1 . For p ≠ 1 / n , n = 1 , 2 , … , the boundary value must locally belong to the local Hardy space h p ( R ) of Goldberg while for p = 1 / n , n = 1 , 2 , … , the answer calls for a new class of atomic Hardy spaces if the vector field is of infinite type at some boundary point.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2007.03.012