Boundary values of functions in vector-valued Hardy spaces and geometry on Banach spaces
The spaces of boundary values of vector-valued functions in Hardy spaces defined by either holomorphic functions on the disk or harmonic functions with maximal function in \(L^ p\) are characterized in terms of vector- valued measures of bounded p-variation (sections 1 and 2). Also, the author extends to the case \(p=1\) a characterization of the Radon-Nikodym property based on the existence of limits at the boundary for harmonic functions with maximal function in \(L^ 1\). In the case \(0<p\leq 1\), the author proves that the UMD property is the necessary and sufficient condition to make the spaces defined by maximal function and by conjugate Poisson kernel coincide.
boundary values of vector-valued functions in Hardy spaces
vector-valued measures of bounded p-variation
scientific article; zbMATH DE number 4075829
scientific article