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- Elias M. Stein
- 2005

S ingular integrals are among the most interesting and important objects of study in analysis, one of the three main branches of mathematics. They deal with real and complex numbers and their functions. In this book, Princeton professor Elias Stein, a leading mathematical innovator as well as a gifted expositor, produced what has been called the most… (More)

- E. M. Stein, G. Weiss
- 2005

p.147, l.–11 Replace the expression for β j by β j = 2(j + 1)(n + 2k − 2j − 4).

- Elias M. Stein, Rami Shakarchi
- 2007

Several related classes of operators on nilpotent Lie groups are considered. These operators involve the following features: (i) oscillatory factors that are exponentials of imaginary polynomials, (ii) convolutions with singular kernels supported on lower-dimensional submanifolds, (iii) validity in the general context not requiring the existence of… (More)

- E M Stein
- Proceedings of the National Academy of Sciences…
- 1961

- ELIAS M. STEIN
- 2010

The aim of this paper is to prove a generalization of a well-known con-vexity theorem of M. Riesz [8]. The Riesz theorem was originally deduced by "real-variable" techniques. Later, Thorin [10], Tamarkin and Zygmund [9], and Thorin [ll] introduced convexity properties of analytic functions in their study of Riesz's theorem. These ideas were put in… (More)

- ZOLTÁN M. BALOGH, JEREMY T. TYSON, BEN WARHURST, Juha Heinonen, E. M. Stein
- 2007

We solve Gromov's dimension comparison problem for Hausdorff and box counting dimension on Carnot groups equipped with a Carnot-Carathéodory metric and an adapted Euclidean metric. The proofs use sharp covering theorems relating optimal mutual coverings of Euclidean and Carnot-Carathéodory balls, and elements of sub-Riemannian fractal geometry associated to… (More)

Let G be a real noncompact semi-simple Lie group with finite center and K a maximal compact sub-group. The symmetric space M = G/K carries a measure invariant under the action of G. The operators which map L(p)(M) continuously into itself and commute with the action of G, can be easily characterized when p = 2 or p = 1. This note gives some results on… (More)

- E. M. STEIN
- 2010