Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.

### Volume 50, Number 3

#### Publication Date: September 1983

On the period map for surfaces with $K^2_S=2, p_g=1, q=0$ and torsion $\mathbf{Z}/2\mathbf{Z}$

P. Oliverio; 561-571

Inequalities for Peano maximal functions and Marcinkiewicz integrals

Sagun Chanillo and Richard L. Wheeden; 573-603

Regularization theorems in Lie algebra cohomology. Applications

A. Borel; 605-623

$L^2$-cohomology of locally symmetric manifolds of finite volume

A. Borel and W. Casselman; 625-647

The uniform central limit theorem for theta sums

W. B. Jurkat and J. W. Van Horne; 649-666

Varieties of low $\Delta$-genus

Tony Horowitz; 667-683

Surfaces with a hyperelliptic hyperplane section

Lawrence Ein; 685-694

On $p$-adic meromorphic functions

Hà Huy Khóai; 695-711

Hypoellipticity of a system of complex vector fields

Mei-Chi Shaw; 713-728

Un exemple de champ magnetique dans $\mathbf{R}^\nu$

Alain Dufresnoy; 729-734

Hilbert transforms for convex curves

Alexander Nagel, James Vance, Stephen Wainger and David Weinberg; 735-744

A special surface in the $4$-quadric

Norman Goldstein; 745-761

Torsion dans le groupe de Chow de codimension deux

Jean-Louis Colliot-Thélène, Jean-Jacques Sansuc and Christophe Soulé; 763-801

The Gauss equations and rigidity of isometric embeddings

Eric Berger, Robert Bryant and Phillip Griffiths; 803-892