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Featured Publication

New Series!  IAS/PCMI and the AMS present:
the Teacher Program Series
Books in this series are designed for mathematics teachers, grades 3–12, to improve knowledge through a problem-based approach.


Introduction to Analytic and Probabilistic Number Theory: Third Edition
Gérald Tenenbaum
This book provides a thorough, self-contained introduction to the analytic and probabilistic methods of number theory.


Mathematics++: Selected Topics Beyond the Basic Courses
Ida Kantor, Jiří Matoušek, and Robert Šámal
This book is a concise introduction to measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology.

The Scholarly Kitchen

by Robert M. Harington D. Phil.
The AMS Associate Executive Director writes about gender diversity in leadership roles in academic publishing.  Find out more at the Scholarly Kitchen.

Bulletin of the AMS

Bulletin of the AMS $L^p$ theory for outer measures and two themes of Lennart Carleson united
( view abstract )
$L^p$ theory for outer measures and two themes of Lennart Carleson united
We develop a theory of $ L^p$ spaces based on outer measures generated through coverings by distinguished sets. The theory includes as a special case the classical $ L^p$ theory on Euclidean spaces as well as some previously considered generalizations. The theory is a framework to describe aspects of singular integral theory, such as Carleson embedding theorems, paraproduct estimates, and $ T(1)$ theorems. It is particularly useful for generalizations of singular integral theory in time-frequency analysis, the latter originating in Carleson's investigation of convergence of Fourier series. We formulate and prove a generalized Carleson embedding theorem and give a relatively short reduction of the most basic $ L^p$ estimates for the bilinear Hilbert transform to this new Carleson embedding theorem.

Browse the archive 1891 - 2015.

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