Approximation of monogenic functions by higher order Szegö kernels on the unit ball and half space

Abstract

We study the adaptive decomposition of functions in the monogenic Hardy spaces \(\mathcal{H}^2\) by higher order Szego kernels under the framework of Clifford algebra and Clifford analysis, in the context of unit ball and half space. This is a sequel and a higher-dimensional generalization of our recent study on the complex Hardy spaces.