**Contemporary Mathematics**

Volume: 277;
2001;
158 pp;
Softcover

MSC: Primary 35; 31;

Print ISBN: 978-0-8218-2745-1

Product Code: CONM/277

List Price: $53.00

Individual Member Price: $42.40

**Electronic ISBN: 978-0-8218-7867-5
Product Code: CONM/277.E**

List Price: $53.00

Individual Member Price: $42.40

# Harmonic Analysis and Boundary Value Problems

Share this page *Edited by *
*Luca Capogna; Loredana Lanzani*

This volume presents research and expository articles by the participants of
the 25th Arkansas Spring Lecture Series on “Recent Progress in the Study of
Harmonic Measure from a Geometric and Analytic Point of View” held at the
University of Arkansas (Fayetteville). Papers in this volume provide clear and
concise presentations of many problems that are at the forefront of harmonic
analysis and partial differential equations.

The following topics are featured: the solution of the Kato conjecture, the
“two bricks” problem, new results on Cauchy integrals on non-smooth curves, the
Neumann problem for sub-Laplacians, and a new general approach to both divergence
and nondivergence second order parabolic equations based on growth
theorems. The articles in this volume offer both students and researchers a
comprehensive volume of current results in the field.

#### Table of Contents

# Table of Contents

## Harmonic Analysis and Boundary Value Problems

- Contents vii8 free
- Preface ix10 free
- The mixed boundary problem in LP and Hardy spaces for Laplace's equation on a Lipschitz domain 112 free
- Sub-elliptic Besov spaces and the characterization of traces on lower dimensional manifolds 1930
- The solution of the Kato problem 3950
- A decomposition of functions with vanishing mean oscillation 4556
- General second order, strongly elliptic systems in low dimensional nonsmooth manifolds 6172
- Growth theorems and Harnack inequality for second order parabolic equations 8798
- Absolute continuity of generalized periodic Schrödinger operators 113124
- The use of Rellich identities on certain nongraph boundaries 127138
- L2 boundedness of the Cauchy integral and Menger curvature 139150

#### Readership

Graduate students and research mathematicians interested in partial differential equations and potential theory.