Atoms and singular integrals on complex domains. (English) Zbl 1295.32020

Krantz, Steven G.

Real Anal. Exch. 38(2012-2013), No. 2, 409-420 (2013).

Summary: We study spaces of homogeneous type, and especially the theory of atoms, on the boundary of a domain in \(\mathbb{C}^n\). 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.

MSC:

32F18	Finite-type conditions for the boundary of a domain
32T25	Finite-type domains
32V35	Finite-type conditions on CR manifolds
32A55	Singular integrals of functions in several complex variables

Keywords:

complex domains; finite type; atomic decomposition; singular integrals