دانلود کتاب Hardy Inequalities on Homogeneous Groups 100 Years of Hardy Inequalities

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Contents......Page 8
Preface......Page 13
Introduction......Page 17
Homogeneous groups......Page 27
Homogeneous quasi-norms......Page 32
Polar coordinates......Page 37
Convolutions......Page 39
Polynomials......Page 42
Radial derivative......Page 51
Euler operator......Page 52
From radial to non-radial inequalities......Page 56
Euler semigroup e-tE*E......Page 58
Stratified Lie groups......Page 62
Extended sub-Laplacians......Page 64
Divergence theorem......Page 65
Green\'s identities for sub-Laplacians......Page 69
Green\'s identities for p-sub-Laplacians......Page 72
Sub-Laplacians with drift......Page 73
Polarizable Carnot groups......Page 76
Heisenberg group......Page 78
Quaternionic Heisenberg group......Page 81
H-type groups......Page 84
Hardy inequality and uncertainty principle......Page 87
Weighted Hardy inequalities......Page 92
Hardy inequalities with super weights......Page 96
Hardy inequalities of higher order with super weights......Page 99
Two-weight Hardy inequalities......Page 100
Critical Hardy inequalities......Page 109
Critical Hardy inequalities......Page 110
Another type of critical Hardy inequality......Page 114
Critical Hardy inequalities of logarithmic type......Page 116
Remainder estimates for Lp-weighted Hardy inequalities......Page 119
Critical and subcritical Hardy inequalities......Page 125
A family of Hardy–Sobolev type inequalities on quasi-balls......Page 126
Improved Hardy inequalities on quasi-balls......Page 132
Stability of Hardy inequalities for radial functions......Page 137
Stability of Hardy inequalities for general functions......Page 138
Stability of critical Hardy inequality......Page 140
Rellich inequality......Page 144
Rellich type inequalities in L2......Page 146
Rellich type inequalities in Lp......Page 152
Stability of Rellich type inequalities......Page 156
Higher-order Hardy–Rellich inequalities......Page 159
Hardy and Sobolev type inequalities......Page 179
Weighted Lp-Sobolev type inequalities......Page 185
Stubbe type remainder estimates......Page 187
Caffarelli–Kohn–Nirenberg inequalities......Page 190
Lp-Caffarelli–Kohn–Nirenberg inequalities......Page 192
Higher-order Lp-Caffarelli–Kohn–Nirenberg inequalities......Page 196
New type of Lp-Caffarelli–Kohn–Nirenberg inequalities......Page 199
Extended Caffarelli–Kohn–Nirenberg inequalities......Page 200
Gagliardo seminorms and fractional p-sub-Laplacians......Page 205
Fractional Hardy inequalities on homogeneous groups......Page 207
Fractional Sobolev inequalities on homogeneous groups......Page 210
Fractional Gagliardo–Nirenberg inequalities......Page 216
Fractional Caffarelli–Kohn–Nirenberg inequalities......Page 217
Lyapunov inequalities on homogeneous groups......Page 227
Lyapunov type inequality for fractional p-sub-Laplacians......Page 228
Lyapunov type inequality for systems......Page 231
Lyapunov type inequality for Riesz potentials......Page 235
Riesz kernels on stratified Lie groups......Page 239
Hardy inequalities for fractional powers of sub-Laplacians......Page 242
Landau–Kolmogorov inequalities on stratified groups......Page 246
Two-weight integral Hardy inequalities......Page 250
Convolution Hardy inequalities......Page 261
Hardy–Littlewood–Sobolev inequalities on homogeneous groups......Page 275
Maximal weighted integral Hardy inequality......Page 279
Chapter 6: Horizontal Inequalities on Stratified Groups......Page 283
Horizontal Lp-Caffarelli–Kohn–Nirenberg inequalities......Page 284
Badiale–Tarantello conjecture......Page 287
Horizontal higher-order versions......Page 289
Horizontal Hardy and Rellich inequalities......Page 291
Critical horizontal Hardy type inequality......Page 292
Two-parameter Hardy–Rellich inequalities by factorization......Page 295
Hardy–Rellich type inequalities and embedding results......Page 304
Horizontal Sobolev type inequalities......Page 310
Horizontal extended Caffarelli–Kohn–Nirenberg inequalities......Page 314
Horizontal Hardy–Rellich type inequalities for p-sub-Laplacians......Page 316
Inequalities for weighted p-sub-Laplacians......Page 318
Horizontal Rellich inequalities for sub-Laplacians with drift......Page 321
Horizontal Picone identities......Page 326
Horizontal anisotropic Rellich type inequality......Page 331
Horizontal Hardy inequalities with multiple singularities......Page 333
Horizontal many-particle Hardy inequality......Page 336
Hardy inequality with exponential weights......Page 340
Chapter 7: Hardy–Rellich Inequalities and Fundamental Solutions......Page 342
Weighted Lp-Hardy inequalities......Page 343
Weighted Lp-Rellich inequalities......Page 348
Two-weight Hardy inequalities and uncertainty principles......Page 352
Rellich inequalities for sub-Laplacians with drift......Page 360
Hardy inequalities on the complex affine group......Page 365
Hardy inequalities for Baouendi–Grushin operators......Page 369
Hardy and Caffarelli–Kohn–Nirenberg inequalities......Page 374
Rellich inequalities......Page 379
L2-Hardy inequality on the half-space......Page 384
Examples of Heisenberg and Engel groups......Page 388
Lp-Hardy inequality on the half-space......Page 391
L2-Hardy inequality on convex domains......Page 393
Lp-Hardy inequality on convex domains......Page 396
Chapter 9: Uncertainty Relations on Homogeneous Groups......Page 400
Definition and assumptions......Page 401
Examples......Page 402
Further position-momentum identities......Page 405
Heisenberg–Kennard and Pythagorean inequalities......Page 406
Heisenberg–Pauli–Weyl uncertainty principle......Page 407
Radial dilations – Coulomb relations......Page 409
Further weighted uncertainty type inequalities......Page 412
Euler–Hilbert–Sobolev spaces......Page 415
Poincaré type inequality......Page 418
Sobolev–Lorentz–Zygmund spaces......Page 419
Bessel–Riesz kernels on homogeneous groups......Page 429
Hardy–Littlewood maximal operator in Morrey spaces......Page 431
Bessel–Riesz operators in Morrey spaces......Page 433
Generalized Bessel–Riesz operators......Page 442
Olsen type inequalities for Bessel–Riesz operator......Page 445
Fractional integral operators in Morrey spaces......Page 446
Olsen type inequalities for fractional integral operators......Page 449
Summary of results......Page 451
Besov type space: Gagliardo–Nirenberg inequalities......Page 453
Generalized Campanato spaces......Page 455
Chapter 11: Elements of Potential Theory on Stratified Groups......Page 461
Boundary value problems on stratified groups......Page 462
Layer potentials of the sub-Laplacian......Page 466
Single layer potentials......Page 467
Double layer potential......Page 469
Traces and Kac\'s problem for the sub-Laplacian......Page 472
Traces of Newton potential for the sub-Laplacian......Page 473
Powers of the sub-Laplacian......Page 476
Extended Kohn Laplacians on the Heisenberg group......Page 482
Powers of the Kohn Laplacian......Page 486
Hardy inequalities with boundary terms on stratified groups......Page 491
Green functions on H-type groups......Page 495
Green functions and Dirichlet problem in wedge domains......Page 496
Green functions and Dirichlet problem in strip domains......Page 501
p-sub-Laplacian Picone\'s inequality and consequences......Page 503
Chapter 12: Hardy and Rellich Inequalities for Sums of Squares......Page 511
Assumptions......Page 512
Examples......Page 513
Divergence formula......Page 515
Green\'s identities for sums of squares......Page 518
Consequences of Green\'s identities......Page 520
Differential forms, perimeter and surface measures......Page 521
Local Hardy inequalities......Page 523
Anisotropic Hardy inequalities via Picone identities......Page 529
Local uncertainty principles......Page 536
Local Rellich inequalities......Page 541
Rellich inequalities via Picone identities......Page 550
Bibliography......Page 554
Index......Page 575