Real Analysis Exchange

Atoms and Singular Integrals on Complex Domains

Steven G. Krantz

Full-text: Open access


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.

Article information

Real Anal. Exchange, Volume 38, Number 2 (2012), 409-420.

First available in Project Euclid: 27 June 2014

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32F18: Finite-type conditions 32T25: Finite type domains
Secondary: 32V35: Finite type conditions on CR manifolds 32A55: Singular integrals 42A50: Conjugate functions, conjugate series, singular integrals 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)

complex domains finite type atomic decomposition singular integrals


Krantz, Steven G. Atoms and Singular Integrals on Complex Domains. Real Anal. Exchange 38 (2012), no. 2, 409--420.

Export citation