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COMPENSATED COMPACTNESS AND PARACOMMUTATORS

Published online by Cambridge University Press:  08 January 2001

LIZHONG PENG  and
M. W. WONG
LIZHONG PENG
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, China; [email protected]
M. W. WONG
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada; [email protected]
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Abstract

The paper provides a new look at compensated compactness and paracommutators. It is shown that there is a one-to-one correspondence between compensated quantities and paracommutators, that the H1-regularity of compensated quantities is equivalent to bounded mean oscillation boundedness of paracommutators, that the weak convergence of compensated quantities is equivalent to vanishing mean oscillation compactness of paracommutators, that the Schatten–von Neumann Sp-property is a natural generalization of vanishing mean oscillation compactness, that the theory of paracommutators provides a ready-made tool for Sp-regularity of compensated quantities, and that the cut-off phenomenon of paracommutators exactly coincides with the vanishing moment properties of the compensated quantities. Some further examples are given.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 505 - 520
Copyright
The London Mathematical Society 2000

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