Spin Geometry, Clifford Analysis, and Joint Seminormality

  • Mircea Martin
Part of the Trends in Mathematics book series (TM)


The first part of this article studies the integral and maximal operators associated with fundamental solutions of Dirac operators on Clifford bundles. The main goal is to obtain explicit estimates for integral transforms of this kind in terms of the corresponding maximal functions. As direct cones-quences of such estimates one derives several quantitative Hartogs-Rosenthal type theorems concerning monogenic approximation on compact sets.

The second part illustrates a Clifford analysis approach to the theory of seminormal systems of Hilbert space operators. The four existing concepts of joint seminormality are reevaluated by assuming that the remainders in some Bochner-Kodaira identities are semidefinite, and a new concept is introduced based on a Bochner-Weitzenböck identity. A rather general singular integral model of jointly seminormal pairs of systems of self-adjoint operators that involves Riesz transforms is presented, and a Putnam type commutator inequality for that model is proved.


Clifford algebras Dirac operators hyponormal operators Putnam’s inequality Riesz transforms 

Mathematics Subject Classification (2000)

Primary: 42B20, 47B20 Secondary: 44A35, 47A13, 47A30 


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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Mircea Martin
    • 1
  1. 1.Department of MathematicsBaker UniversityBaldwin CityUSA

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