Atoms and Singular Integrals on Complex Domains

Abstract

We study spaces of homogeneous type, and especially the theory of atoms, on the boundary of a domain in \(\CC^n\). We are particularly interested in atoms for small \(p\), which must satisfy a higher-order moment condition. We have an axiomatic presentation of these ideas which avoids a lot of the usual nasty calculations. Examples show that this new theory is consistent with existing particular instances of atoms.