• Publications
  • Influence
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 anExpand
  • 98
  • 19
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. DiffeomorphismExpand
  • 126
  • 18
  • PDF
On certain maximal functions and approach regions
If f E L’(iR”) and u(x, y) is the Poisson integral of J; a classical theorem of Fatou [2] asserts that u has nontangential limits almost everywhere on R”. Littlewood [5], and later Zygmund [9],Expand
  • 98
  • 14
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 pseudodifferentialExpand
  • 119
  • 10
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 aExpand
  • 79
  • 9
  • 51
  • 7
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 weExpand
  • 203
  • 7
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 aExpand
  • 90
  • 6
  • PDF