BOUNDARY VALUES OF VECTOR-VALUED HARDY SPACES ON NONSMOOTH DOMAINS AND THE RADON-NIKODYM PROPERTY

作者：Ocampo Salgado Hugo^*; Rivera Noriega Jorge; Martin Luis San

来源：Banach Journal of Mathematical Analysis, 2016, 10(3): 523-546.

DOI：10.1215/17358787-3607222

• vector-valued Hardy spaces
• Radon-Nikodym property
• Fatou-type theorems
• Lipschitz domains
• noncylindrical domains

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 p >= 1, (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 V-X(p) 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 R-n x (0, infinity).

• 出版日期2016-7