We define Hardy spaces of functions taking values on a Banach space 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 in terms of the existence of nontangential limits of -valued functions in the corresponding Hardy space with index , (b) to identify the function of the boundary values of in the Hardy space with index with an element in the space of measures of -bounded variation in the absence of the Radon–Nikodym property of . This extends similar results already known on the unit disk of and the semispace .
"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. https://doi.org/10.1215/17358787-3607222