Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms (Memoirs of the American Mathematical Society) - Softcover

Alexander Nagel (author), Fulvio Ricci (author), Elias M. Stein (author) & Stephen Wainger (author)

 
9781470434380: Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms (Memoirs of the American Mathematical Society)
Softcover
ISBN 10: 1470434385 ISBN 13: 9781470434380
Publisher: American Mathematical Society, 2018

Synopsis

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.

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About the Author

Alexander Nagel, University of Wisconsin-Madison, WI.

Fulvio Ricci, Scuola Normale Superiore, Pisa, Italy.

Elias M. Stein, Princeton University, NJ.

Stephen Wainger, University of Wisconsin-Madison, WI.

"About this title" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
2018
Language
English
ISBN 10 
1470434385
ISBN 13 
9781470434380
Binding
Paperback
Number of pages
141