The authors study algebras of singular integral operators on $/mathbb R^n$ and nilpotent Lie groups that arise when considering the composition of Calderon-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems. These algebras are characterized in a number of different but equivalent ways: in terms of kernel estimates and cancellation conditions, in terms of estimates of the symbol, and in terms of decompositions into dyadic sums of dilates of bump functions. The resulting operators are pseudo-local and bounded on $L^p$ for $1 /lt p /lt /infty $. While the usual class of Calderon-Zygmund operators is invariant under a one-parameter family of dilations, the operators studied here fall outside this class, and reflect a multi-parameter structure.

Book Information
ISBN 9781470434380
Author Alexander Nagel
Format Paperback
Page Count 141
Imprint American Mathematical Society
Publisher American Mathematical Society