AN ANALYTIC RADON-NIKODYM PROPERTY RELATED TO SYSTEMS OF VECTOR-VALUED CONJUGATE HARMONIC FUNCTIONS AND CLIFFORD ANALYSIS

EREZ-ESTEVA Abstract. The purpose of this paper is to study the existence of boundary limits of systems of conjugate harmonic functions defined in the unit ball in Rn and with values in a real Banach space E. We approach this problem using the language of Clifford Analysis and consider Hardy spaces in the unit ball of Rn of monogenic functions with values in a Banach Clifford module. In terms of the so called Monogenic Measures on the sphere, we define a Monogenic Radon-Nikodym property which is linked with the existence of radial limits of vector-valued monogenic functions as in the holomorphic case. For Banach lattices we adapt the proof by A.V. Bukhvalov and A.A. Danilevich to show that for any real Banach lattice E, the Clifford module X = An E has the Monogenic Radon-Nikodym property (An is the Clifford algebra) if and only c0 is not a subspace of E, which is equivalent to the Analytic Radon-Nikodym property of EC.