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July 2016 Boundary values of vector-valued Hardy spaces on nonsmooth domains and the Radon–Nikodym property
Hugo Ocampo-Salgado, Jorge Rivera-Noriega, Luis San Martin
Banach J. Math. Anal. 10(3): 523-546 (July 2016). DOI: 10.1215/17358787-3607222


We define Hardy spaces of functions taking values on a Banach space X over nonsmooth domains. The types of functions we consider are harmonic functions on a starlike Lipschitz domain and solutions to the heat equation on a time-varying domain. Our purpose is twofold: (a) to characterize the Radon–Nikodym property of the Banach space X in terms of the existence of nontangential limits of X-valued functions u in the corresponding Hardy space with index p1, (b) to identify the function of the boundary values of u in the Hardy space with index p>1 with an element in the space VXp of measures of p-bounded variation in the absence of the Radon–Nikodym property of X. This extends similar results already known on the unit disk of C and the semispace Rn×(0,).


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Hugo Ocampo-Salgado. Jorge Rivera-Noriega. Luis San Martin. "Boundary values of vector-valued Hardy spaces on nonsmooth domains and the Radon–Nikodym property." Banach J. Math. Anal. 10 (3) 523 - 546, July 2016.


Received: 18 March 2015; Accepted: 7 November 2015; Published: July 2016
First available in Project Euclid: 6 June 2016

zbMATH: 1357.46034
MathSciNet: MR3509883
Digital Object Identifier: 10.1215/17358787-3607222

Primary: 46B22
Secondary: 31A15, 31A20, 46G10

Rights: Copyright © 2016 Tusi Mathematical Research Group


Vol.10 • No. 3 • July 2016
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