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Harmonic Analysis and Partial Differential Equations
Edited by: Mario Milman and Tomas Schonbek
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Contemporary Mathematics
1990; 129 pp; softcover
Volume: 107
ISBN-10: 0-8218-5113-6
ISBN-13: 978-0-8218-5113-5
List Price: US$48
Member Price: US$38.40
Order Code: CONM/107
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This book brings together ten papers presented at the Conference on Harmonic Analysis and Partial Differential Equations, held in April 1988 at Florida Atlantic University. The papers illuminate the relationship between harmonic analysis and partial differential equations and present results of some of the foremost experts in these areas. Among the topics covered are: application of fully nonlinear, uniformly elliptic equations to the Monge Ampère equation; estimates for Green functions for the purpose of studying Dirichlet problems for operators in non-divergence form; an extension of classical potential theory to the case of nonsmooth domains; the relation between Riesz potentials and maximal fractional operators due to Muckenhoupt and Wheeden; and the Lax-Phillips scattering theory applied to the double Hilbert transform. Directed at research mathematicians and graduate students, the papers require knowledge of the classical tools of analysis, such as measure theory, Sobolev spaces, and potential theory.

Table of Contents

  • B. Barcelo, L. Escauriaza, and E. Fabes -- Gradient estimates at the boundary for solutions to nondivergence elliptic equations
  • L. A. Caffarelli -- Interior regularity of solutions to Monge Ampère equations\
  • M. Cotlar and C. Sadosky -- The Helson-Szegö theorem in \(L^p\) of the bidimensional torus
  • B. E. Dahlberg and G. Verchota -- Galerkin methods for the boundary integral equations of elliptic equations in nonsmooth domains
  • R. Fefferman -- Some applications of Hardy spaces and BMO in harmonic analysis and partial differential equations
  • B. Jawerth, C. Perez, and G. Wellland -- The positive cone in Triebel-Lizorkin spaces and the relation among potential and maximal operators
  • R. Johnson -- Changes of variable and \(A_p\) weights
  • C. E. Kenig -- Progress on two problems posed by Rivière
  • A. C. Lazer and P. J. McKenna -- Fredholm theory for periodic solutions of some semilinear P.D.E.s with homogeneous nonlinearities
  • W. A. Strauss -- Stability of solitary waves
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