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REDUCTION OF CALDERÓN COMMUTATORS

Published online by Cambridge University Press:  01 January 1998

PAUL S. MUHLY  and
JINGBO XIA
PAUL S. MUHLY
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA
JINGBO XIA
Affiliation:
Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14214, USA
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Abstract

Let A1,…, An be Lipschitz functions on R such that A′1,…, A′n∈VMO. We show that on any bounded interval, the Calderón commutator associated with the kernel (A1(x)−A1(y)) …(An(x) −An(y))/(x−y) n+1 is a compact perturbation of −πiHMA′1… A′n, where H is the Hilbert transform.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 1 , January 1998 , pp. 67 - 72
Copyright
© The London Mathematical Society 1998

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