Reproducing kernels of harmonic Besov spaces on the ball

Abstract

Besov spaces of harmonic functions on the unit ball of Rn are defined by requiring sufficiently high-order derivatives of functions lie in harmonic Bergman spaces. We compute the reproducing kernels of those Besov spaces that are Hilbert spaces. The kernels turn out to be weighted infinite sums of zonal harmonics and natural radial fractional derivatives of the Poisson kernel. To cite this article: S. Gergün et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.