Christ M., Kenig C.E., Sadosky C. Harmonic Analysis and Partial Differential Equations: Essays in Honor of Alberto P. Calderon
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354
Fefferman-Stein sharp function, 211
free boundary, 264
Gauss-Bonnet formula, 130
Gaussian normal measure, 153
geometry, conformal, 127
global solutions, 244
gradient, generalized, 288
Hardy spaces H°, 3
Hardy-Littlewood maximal function,
27
harmonic maps, 137
harmonic measure, 99
Harnack inequality, 270
Hausdorff measure, 288
heat equation, nonlinear, 242
heat kernel, 275
Hilbert space valued functions, 219
Hilbert transform, 5, 51; ergodic,
28; multiple, 208
Hopf lemma, 264
index theorem: Atiyah-Patodi-Singer
problems, 278; Atiyah-Singer
index theorem, 10, 276
information compression, 166
integration by parts, 156
inverse conductivity problem, 304
inverse problems, 295
isoperimetric inequalities, 286
KAM theory, 90
Lagrangian coordinates, 121
Laplacian, first-order perturbations
of, 321
Lebesgue point, 286
Lipschitz curve, 14
Lipschitz functions, 286
Littlewood-Paley theory, 3
locally conformally flat, 142
locally linearly contractible, 289
log-determinant functional, 137
Lyapunov-Schmidt method, 69
magnetic potential, 321
Marcinkiewicz multipliers, 208
Index
Markov chain, 111; stationary, 32
Martingale theory, 99
maximal ergodic inequality, 28
maximal function, strong, 207
maximum principle, 263
Melnikov problem, 90
Menger curvature, 183
metric spaces, 285
metric, characteristic polynomials
for, 277
modulation model, 164
Monge-Ampere equation, 117
monotonicity, 263
Moser's inequality, 136
moving plane, 134, 263
multiplier, 50
Navier-Stokes equations, 253
Newton iteration procedure, 71
nodal sets, 223
noise, low level, 164
nonlinear equation, fully, 118
optics, complex geometrical, 295
optimal control, 227
Oseledets question, 35
Paneitz operator, 127
para-aceretive function, 187
parabolic equations, 16
para-product, 12
partial differential equations,
subelliptic, 17, 199
partial differential operator, fourth
order, 127
path space, 157
periodic solutions, 69
Poincare inequalities, 286
pointwise ergodic theorem, 27
Polyakov formula, 138
potential operator, 287
pseudodifferential operators, 10,
199, 328; weakly parametric, 280
quasiconvex functions, 101
rank-one convex function, 101
real-variable theory, 2
rectangle atom, 210
Index
rectangles, two parameter family of,
214
rectifiability, 183, 191
regularity theory, 118
renormalization, L51
resolvent kernel, 275
Riesz transforms, 6 L51
rotations, 121
sawtooth domain, 4
Schrodinger equation, 300;
nonlinear, 257
self-similar solution, 241. conver-
gence to, 254
sharp operator, 211
sharp weighted inequalities, 218
singular integrals along surfaces,
213_
singular sites, 73
singularities, resolution of, 244
sliding method, 264
small divisor problems, 74
Sobolev spaces, 256
spaces of homogeneous type, 255
speaker identification, 153
square functions, 36 estimates, 57
Stein's ergodic theorem, 36
stochastic integrals, 99 151
structure equation, 158
subband filtering schemes, 174
subordinate: conditionally differen-
tially, 102. differentially, 99
subpositive family, 51
355
symbol, 7
symmetric spaces, 17
symmetry, 263
symplectic subunit balls, 199
synchrosqueezing, 171
tangent processes, 158
Tauberian theorem, 275
trace formula, 277
transference: Calder6n transference
principle, 28 transference cou-
ples, 49. transference principles,
27
trigonometric series, 1
unique continuation, 226. 233
uniqueness for boundary operators,
233.
Vitushkin's conjecture, 186
wave equations, nonlinear, 69; non-
llamiltonian, 84
wavelet transform, 164
wavelet transform, continuous:
squeezing, 169
weak-type inequality, 41
weighted maximal estimates, 42
Yamabe problem, 131
zeta function, 275
zeta functional determinant, 13.8
Mathematics
A
Iberto P. CalderOn (1920-1998) was one of the twentieth century's
leading mathematical analysts. Two years befon. his death, more
than 300 mathematicians from around the world gathered in
Chicago for a conference held in Calderon's honor, presenting the papers
on harmonic analysis and partial differential equations from which this vol-
ume originated. Containing timely syntheses of several major fields of
mathematics and original research articles contributed by some of the finest
scholars in these areas, this book serves as an even more fitting tribute.
With contributions by:
Elias M. Stein
Stephane Macs
Alexandra Bellow
Guy David
Earl Berkson
Charles Feffetman
Maciej PaluszyrIski
Robert A. Fefferman
Guido Weiss
David Jerison
Jean Bourgain
Gilles Lebeau
Donald L. Burkholder
Yves Meyer
Luis A. Caffarelli
Louis Nirenbt rg
Sun-Yung A. Chang
Robert Seeley
A. B. Cruzeiro
Stephen Semmes
P. Malliavin
and Gunther Uhlmann
Ingrid Daubechies
as well as Calder6n's remarks to the assembled conference.
Michael Christ is professor of mathematics at the University of California,
Berkeley. Carlos E. Kenig is
the Louis Block Distinguished Service
Professor of Mathematics at the University of Chicago. Cora Sadosky is
professor of mathematics at Howard University.
The University of Chicago Press
www.press.uchicago.edu
ISBN 0-226-10455-9
90000
9