Functional analysis, harmonic analysis, and image processing: in honor of Bjorn Jawerth

Cover......Page 1
Title page......Page 4
Contents......Page 6
Preface......Page 8
Björn David Jawerth (1952–2013)......Page 10
 1. Introduction and preliminaries......Page 16
 2. Interplay between interpolation and extrapolation......Page 25
 3. Stability of weighted Δ-functors on ��_{��,��}-spaces......Page 34
 4. Strong extrapolation spaces......Page 42
 5. Probabilistic moment problem......Page 44
 6. Extrapolation of operators with a quasi-Banach target space......Page 55
 References......Page 59
 1. Introduction......Page 64
 2. The classical uncertainty principle inequality for ��²(ℝ^{��})......Page 67
 3. Hardy type inequalities......Page 69
 4. Weighted Fourier transform norm inequalities......Page 72
 5. Uncertainty principle inequalities......Page 77
 6. An uncertainty principle inequality for Hilbert spaces......Page 80
 7. Epilogue......Page 83
 References......Page 84
The discrete Calderón reproducing formula of  Frazier and Jawerth......Page 88
 1. The Continuous Calderón Reproducing Formula......Page 90
 2. The Discrete Calderón Reproducing Formula......Page 98
 3. Characterization of function spaces, atoms, and molecules......Page 104
 4. Almost orthogonality and almost diagonal operators......Page 108
 5. Concluding remarks......Page 112
 References......Page 113
 1. Introduction and statements of main results......Page 118
 2. Preliminary Results......Page 128
 3. Pointwise Definition of the Convolution......Page 131
 4. Maximal Inequalities......Page 135
 5. Proof of Characterisation Theorems......Page 140
 6. Appendix......Page 147
 References......Page 149
 1. Introduction......Page 152
 2. Preliminaries......Page 155
 3. Decomposable MI spaces in ��²(Ω,ℋ)......Page 157
 4. Approximation problems......Page 159
 5. Application to SI spaces in LCA groups......Page 166
 6. Totally decomposable MI spaces and translation-invariant spaces......Page 169
 7. Acknowledgments......Page 171
 References......Page 172
 1. Introduction......Page 176
 2. Preliminaries......Page 177
 3. Homogeneous mixed-norm Besov spaces......Page 179
 4. The ��-transform......Page 184
 5. Inhomogeneous mixed-norm Besov spaces......Page 188
 6. Appendix......Page 190
 References......Page 192
 1. The Frazier-Jawerth Atomic Characterizations......Page 194
 2. Coorbit Theory......Page 200
 3. Decomposition Spaces......Page 203
 4. Abstract and Concrete Wavelet Theory......Page 213
 References......Page 221
Traces and extensions of weighted Sobolev and  potential spaces......Page 226
 1. Introduction......Page 227
 2. Decomposition of Weighted Function Spaces......Page 230
 3. Traces and Extensions......Page 238
 References......Page 242
 Introduction......Page 244
 1. Function spaces......Page 245
 2. Continuous embeddings......Page 251
 3. Compact embeddings of weighted spaces: a model case......Page 254
 References......Page 259
 Introduction......Page 264
 Overview of the Tracking Algorithm......Page 266
 2. Selection of features and search regions......Page 268
 3. Finding the displacement of a feature region within the corresponding search region......Page 270
 5. Discussion......Page 273
 7. Acknowledgements......Page 276
 References......Page 277
 1. Introduction......Page 280
 2. Background......Page 282
 4. Application. Extending holomorphic sections......Page 285
 References......Page 290
 1. Introduction......Page 292
 2. Preliminaries......Page 293
 3. Maximal operator on associate spaces......Page 297
 4. Proof of Theorem 1.1......Page 299
 5. Proof of Lemma 4.1......Page 301
 6. Concluding remarks and open questions......Page 307
 References......Page 308
 1. Statement of the Result......Page 310
 3. A Reformulation Using the Metric ��......Page 311
 4. Preliminary Estimates......Page 313
 5. Proof of the Theorem......Page 314
 6. Final Remarks......Page 315
 References......Page 316
 1. Introduction......Page 318
 2. The Hardy Space ��¹(\R)......Page 320
 3. Characterizations of BMO(\R)......Page 325
 References......Page 328
 1. Introduction......Page 330
 2. Capacity-type argument......Page 332
 3. Proof by partition of domain and range......Page 334
 4. Proof by the wavelet decomposition......Page 335
 5. Proof via the Littlewood-Paley decomposition......Page 336
 References......Page 337
 1. Introduction and motivation......Page 340
  2.1. Preliminaries and inhomogeneous spaces......Page 343
  2.2. Spaces with negative smoothness......Page 346
  2.3. Spaces in the distinguished strip......Page 351
  3.1. Embeddings......Page 357
  3.2. Global inequalities for heat equations......Page 360
  3.3. Hardy inequalities......Page 361
  3.4. Multiplication algebras......Page 363
  3.5. Examples I: Riesz kernels......Page 364
  3.6. Examples II: Mixed Riesz kernels......Page 368
 References......Page 369
 1. Introduction......Page 372
 2. Besov spaces of isotropic and dominating mixed smoothness......Page 374
 3. The main results......Page 376
 4. Proofs......Page 379
 References......Page 397
 1. Introduction......Page 400
 2. Constructions......Page 403
 3. Analysis of the IRLS algorithm......Page 408
 4. Numerics......Page 414
 References......Page 419
Back Cover......Page 422