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Reduction of Calderón Commutators
Author(s) -
Muhly Paul S.,
XIA JINGBO
Publication year - 1998
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460939700369x
Subject(s) - mathematics , commutator , lipschitz continuity , bounded function , mathematics subject classification , perturbation (astronomy) , pure mathematics , hilbert transform , kernel (algebra) , interval (graph theory) , mathematical analysis , combinatorics , algebra over a field , statistics , spectral density , physics , lie conformal algebra , quantum mechanics
Let A 1 ,…, A n 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 ( A 1 ( x )− A 1 ( y )) … ( A n ( x ) − A n ( y ))/( x − y ) n 1 is a compact perturbation of ‐ π i H M A 1 ′ … A n ′, where H is the Hilbert transform. 1991 Mathematics Subject Classification 47B38, 47B47, 47G10, 45E99.