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Singular Integrals with Flag Kernels and Analysis on Quadratic CR Manifolds
Abstract 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
Singular and maximal Radon transforms: analysis and geometry
Part 2. Geometric theory 8. Curvature: Introduction 8.1. Three notions of curvature 8.2. Theorems 8.3. Examples 9. Curvature: Some details 9.1. The exponential representation 9.2. Diffeomorphism
Convex hypersurfaces and Fourier transforms
Hilbert transforms and maximal functions along curves and surfaces, spectral synthesis problems, and the study of certain operators related to hyperbolic partial differential and pseudodifferential
On the product theory of singular integrals
We establish Lp-boundedness for a class of product singular integral operators on spaces M = M1 x M2 x . . . x Mn. Each factor space Mi is a smooth manifold on which the basic geometry is given by a
On Hilbert transforms along curves
Tf is the Hubert transform of ƒ along the curve y{t). E. M. Stein [2] raised the following general question: For what values of/? and what curves y(t) is Tf a bounded operator in Z7? If y(t) is a
Estimates for the Bergman and Szegö kernels in $\mathbf{C}^2$
The purpose of this paper (some of whose conclusions were announced in [NRSW]) is to study the Bergman and Szegd projection operators on pseudoconvex domains Q of finite type in C2. The results we