Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms

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

Buch | Softcover

141 Seiten

2019
American Mathematical Society (Verlag)
978-1-4704-3438-0 (ISBN)

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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.

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.

Introduction
The Classes $/mathcal P(/mathbf E)$ and $/mathcal M(/mathbf E)$
Marked partitions and decompositions of $/mathbb R^N$
Fourier transform duality of kernels and multipliers
Dyadic sums of Schwartz functions
Decomposition of multipliers and kernels
The rank of $/mathbf E$ and integrability at infinity
Convolution operators on homogeneous nilpotent Lie groups
Composition of operators
Convolution of Calderon-Zygmund kernels
Two-flag kernels and multipliers
Extended kernels and operators
The role of pseudo-differential operators
Appendix I: Properties of cones $/Gamma (/mathbf A)$
Appendix II: Estimates for homogeneous norms
Appendix III: Estimates for geometric sums
Bibliography.

Erscheinungsdatum	04.12.2018
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	235 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-3438-5 / 1470434385
ISBN-13	978-1-4704-3438-0 / 9781470434380
Zustand	Neuware