Vector-valued Hardy spaces in non-smooth domains |
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Authors: | Salvador Pé rez-Esteva |
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Affiliation: | a Instituto de Matemáticas - Unidad Cuernavaca, Universidad Nacional Autónoma de México, Apdo. Postal 273-3, Cuernavaca Mor. CP 62251, Mexico b Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001. Col. Chamilpa, Cuernavaca Mor. CP 62209, Mexico |
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Abstract: | We characterize the Radon-Nikodým property of a Banach space X in terms of the existence of non-tangential limits of X-valued harmonic functions u defined in a domain D⊂Rn, n>2, with Lipschitz boundary and belonging to maximal Hardy spaces. This extends the same result previously known for the unit disk of C. We also prove an atomic decomposition of the Borel X-valued measures in ∂D that arise as boundary limits of X-valued harmonic functions whose non-tangential maximal function is integrable with respect to harmonic measure of ∂D. |
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Keywords: | Radon-Nikodý m property Vector-valued harmonic functions Fatou theorems Atomic decompositions of Hardy spaces |
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