Singular Integrals with Flag Kernels and Analysis on Quadratic CR Manifolds
✍ Scribed by Alexander Nagel; Fulvio Ricci; Elias M Stein
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 499 KB
- Volume
- 181
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
We study a class of operators on nilpotent Lie groups G given by convolution with flag kernels. These are special kinds of product-type distributions whose singularities are supported on an increasing subspace (0
We show that product kernels can be written as finite sums of flag kernels, that flag kernels can be characterized in terms of their Fourier transforms, and that flag kernels have good regularity, restriction, and composition properties.
We then apply this theory to the study of the g b -complex on certain quadratic CR submanifolds of C n . We obtain L p regularity for certain derivatives of the relative fundamental solution of g b and for the corresponding Szego projections onto the null space of g b by showing that the distribution kernels of these operators are finite sums of flag kernels.
2001 Academic Press
Contents.
1. Introduction.
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Products and flags: Kernels and multipliers. 3. Cauchy Szego kernels for polyhedral tube domains.
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Quadratic submanifolds 7 A /C n _C m . 5. Fourier analysis on the groups G A .
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Analysis of the b complex on G A .
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Further analysis of the operators g J on G A . 8. Singularities of the Szego projection on G A .