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Stein E.M. Ч Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscilattory Integrals
Stein E.M. Ч Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscilattory Integrals



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Ќазвание: Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscilattory Integrals

јвтор: Stein E.M.

язык: en

–убрика: ћатематика/јнализ/ѕродвинутый анализ/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1993

 оличество страниц: 695

ƒобавлена в каталог: 02.04.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Commutators      179
Commutators, Calderon      308Ч312 324
Compensated compactness      137
cones      58 132 447Ч449 461
Cones and spheres      459
Cones, aperture      58 62 93 124Ч127 183Ч184
Conjugate functions and $H^p$      120Ч123 133
Continuity in measure      456Ч458
CotlarТs lemma      279Ч282 318
CotlarТs lemma for integrals      318
Covering lemmas      4 84 465
Covering lemmas, Besicovitch      44
Covering lemmas, Borel Ч Cantelli      442Ч443
Covering lemmas, Vitali      8 12 84
Covering lemmas, Whitney decomposition      14Ч17 60 76 102 206
Critical points      334 341
Critical points, absence      331 341
Critical points, degeneracy      344
Critical points, degenerate      332 334 342
Critical points, nondegenerate      344 380
Curvature      5
Curvature and averages      467Ч469
Curvature and Fourier transforms      330
Curvature, cinematic      519Ч520 (see also УFinite typeФ)
Curvature, Gaussian      348 351 360Ч363 494Ч497
Curvature, principal      348 351 360Ч361 365
Curvature, rotational      494Ч497 500 517
Curvature, total      348
Differentiation of integrals      13 44 65 433 441 455
Differentiation of integrals over hypersurfaces      469 509
Differentiation of integrals over submanifolds      492Ч493
Dilations (non-isotropic)      10 37 45 186 277 473 478 486 514 530 541 618
Dini modulus      29 34 72 80 83 481
Dirichlet problem      24 223Ч225 590 629
Dirichlet problem for $\bar{\partial}$      641Ч642
Distance      see УQuasi-distanceФ
Distributional inequalities      23 69 151Ч155 184 188 206Ч209
Doubling measures      8 12 39Ч41 151 196 218
Doubling measures and Zygmund condition      225
Duality, $H^1$ and BMO      142Ч144 163Ч165 178 183
Duality, $H^p$ and $\Lambda_{\gamma}$      130
Duality, $\mathcal{N}$ and $\mathcal{C}$      59Ч61 63 77 161Ч163
Duality, $\mathcal{N}^p$ and $\mathcal{N}^q$      181
Duality, inequalities      59 146Ч147 161Ч163
Duality, VMO and $H^1$      180
Dyadic cubes      149
Dyadic decomposition      241Ч243 253Ч257 403
Dyadic decomposition and square functions      267
Dyadic decomposition for $S^m$      243Ч245 253Ч257
Dyadic decomposition for $S^m_{1,1}$      271Ч275
Dyadic decomposition for singular integrals      246Ч247 295Ч296
Dyadic decomposition in $\mathbb{R}^1$      501 506
Dyadic decomposition, nondyadic decompositions      282Ч285 319
Dyadic decomposition, second      403Ч406 419 522Ч523
Eikonal equation      425
Elliptic operators      230Ч231 241 266
Elliptic operators and weights      223Ч225
entropy      83
Euclidean balls      9
Euclidean measure      9
Exponential integrability      144Ч146 154Ч155 184
Exponential sums      373
Fatou theorem      119Ч120 133
Finite type      350Ч351
Finite type and vector fields      516
Fourier integral operators      173 375Ч376 394Ч412 424Ч429
Fourier integral operators and $H^p_{loc}$      136 429
Fourier integral operators and averages over hypersurfaces      360 496 517
Fourier integral operators and fractional integration      399Ч401 428Ч429
Fourier integral operators and pseudo-differential operators      395 402Ч403
Fourier integral operators in $\mathbb{R}^1$      430
Fourier integral operators in $\mathbb{R}^2$      519Ч523
Fourier integral operators on $H^1$      402Ч405 410Ч411 428
Fourier integral operators on $L^2$      397Ч398
Fourier integral operators on $L^p$      399 402 410Ч412
Fourier integral operators on $L^p_k$      429
Fourier integral operators on $L^{\infty}$      411 (see also УPhase functionsФ)
Fourier integral operators on $\Lambda_{\gamma}$      429
Fourier integral operators, adjoints      400 410
Fourier integral operators, examples      394Ч396
Fourier integral operators, extended      424Ч425
Fourier integral operators, frequency decomposition      403Ч410
Fourier integral operators, kernels      396
Fourier integral operators, kernels in BMO      427
Fourier integral operators, sharp exponents      426 428
Fourier integral operators, singular set $\Sigma_x$      396 403
Fourier transform      3 228 557
Fourier transform and oscillatory integrals      378
Fourier transform of surface-carried measure and $S^m$      360
Fourier transform of surface-carried measure and singular integrals      372Ч373
Fourier transform of surface-carried measure, sphere      174 347Ч348
Fourier transform of surface-carried measure, unbounded      363Ч364
Fourier transform of surface-carried measures      347Ч351 360Ч364
Fourier transform of surface-carried measures and averages over hypersurfaces      468
Fourier transform of surface-carried measures and averages over submanifolds      468
Fourier transform of surface-carried measures and number theory      362Ч363
Fourier transform of surface-carried measures and principal curvatures      360Ч361 365
Fourier transform of surface-carried measures and real-variable structures      361 (see also УRestriction theoremsФ)
Fourier transform of surface-carried measures, curvature has zeros      360Ч362
Fourier transform of surface-carried measures, curved hypersurfaces      348Ч350 360
Fourier transform of surface-carried measures, finite type      350Ч351 353 475 479 492
Fourier transform of surface-carried measures, homogeneous      363Ч364
Fourier transform of surface-carried measures, hyperplanes      351
Fourier transform of surface-carried measures, measure in $L^p(d\sigma)$      372Ч373
Fourier transform of surface-carried measures, real analytic      361
Fourier transform on $H^n$      569Ч573
Fourier transform, convergence      388Ч390 423
Fourier transform, measures of bounded variation      420 (see also УMultipliersФ)
Fourier transform, nondyadic decompositions      282Ч285 319
Fourier transform, radial functions      430
Fractional integration      353Ч354 414
Fractional integration and $H^p$      136
Fractional integration and BMO      178
Fractional integration and Fourier integral operators      399Ч401 428Ч429
Fractional integration and real-variable structures      45
Fractional integration on $L^{p,q}$      265
Fractional integration, imaginary order      33 46
Freeing of monomials      see УLifting techniqueФ
Freezing principle      230Ч231
Functional calculus      231
G-function      47 524
Garding inequalities      321
Gaussian kernel      24
Global $\gamma$-density      62 126
H-type groups      636
Haar basis      173 190
Haar basis, generalized      312Ч316
Hardy Ч Littlewood Ч Sobolev theorem      see УFractional integrationФ
Harmonic measure      41 224Ч225
Hausdorff Ч Young inequality      583
Heat equation      24 276
Heat equation on $H^n$      632Ч633 642Ч643
Helson Ч Szego theorem      225Ч227
Hermite expansions      571Ч573 582Ч584
Hermite operator      549 571 579 598
Hessian determinant      377 384
Hessian determinant and rotational curvature      496
Hessian determinant, zeros      412 415
Hilbert transform      3 26 225Ч227 389 424
Hilbert transform and Cauchy integral      311
Hilbert Ч Schmidt class      554Ч556 570Ч571
Hilbert Ч Schmidt norm      415
Homogeneous dimension      478 620 638
Homogeneous distributions      45 262Ч263
Homogeneous groups      11 83 186 618Ч627 635Ч641
Homogeneous groups, balls $B(x,\delta)$      620
Homogeneous groups, dilations      618 621 637
Homogeneous groups, examples      620Ч621
Homogeneous groups, Haar measure      619
Homogeneous groups, Lie algebras      621Ч622 635Ч637
Homogeneous groups, lifting technique      639Ч641
Homogeneous groups, maximal functions      638
Homogeneous groups, nilpotence      621
Homogeneous groups, norm $\rho$      619 638
Homogeneous groups, singular integrals      622Ч627
Hyperbolic equations      372 395 425 428 429
Hypoellipticity      39 604
Infinite constant      304
Interpolation of operators and $H^p$      137 185
Interpolation of operators and $\Lambda_{\gamma}$      255
Interpolation of operators and $\Lambda_{\gamma}^{p,q}$      264
Interpolation of operators and BMO      173Ч177
Interpolation of operators, averaging operators      371
Interpolation of operators, complex $L^p$      384Ч385
Interpolation of operators, Fourier integral operators      410Ч412
Interpolation of operators, Fourier restriction      352 365
Interpolation of operators, Marcinkiewicz      14 22 36 265 465
Interpolation of operators, maximal averages      14 479Ч482 487Ч489 503 507 518Ч519
Interpolation of operators, oscillatory integrals      381Ч386
Interpolation of operators, singular integrals      22 36 514
Iwasawa decomposition      621 637
John Ч Nirenberg inequality      144Ч146 154Ч155 179
Jump theorem      580
Kakeya needle problem      434 454Ч455
Klein Ч Gordon equation      372
Kohn Laplacian $\square_b$      592Ч593 596Ч597
Kohn Laplacian $\square_b$ on functions      615Ч618
Kohn Laplacian $\square_b$ on pseudoconvex domains      639
Lagrangian distributions      429
Laguerre functions      584
Laplace Ч Beltrami operator      431
Laplacian $(\Delta,\square)$      24 590 592 629
Lattice points, distribution      362
Layer potentials      224
Levi form      593
Lewy operator      611Ч618
Lewy operator, unsolvable equations      612Ч615
Lifting technique      468 513Ч517
Lifting technique and homogeneous groups      639Ч641
Lifting technique, freeing of monomials      477Ч478
Lifting technique, method of descent      483Ч486 490Ч491
Lifting technique, universal variety      477Ч478
Lipschitz domains      137 223Ч225 310Ч316
Littlewood Ч Paley decomposition      see УDyadic decompositionФ
LlogL      see УOrlicz spacesФ
Local smoothing      521Ч523
Local solvability      604 611
Marcinkiewicz integral      76
Martingales      151 187Ч190
Martingales and real-variable structures      189
Martingales, dyadic      187
Maximal functions      3 7Ч14 49Ч75 87Ч101 433Ч434 440Ч449 455Ч511
Maximal functions and balls $M_B$      65Ч69 78Ч79
Maximal functions and sets $M_C$      433 441
Maximal functions and singular integrals      34Ч36 157Ч158
Maximal functions and weights      195 198Ч203
Maximal functions on $H^p$      87Ч112
Maximal functions on $L^1$      13Ч14 43 51Ч53 72 84 446 458
Maximal functions on $L^2$      317Ч318
Maximal functions on $L^p$      441 445
Maximal functions on BMO      179
Maximal functions on homogeneous groups      638
Maximal functions, $M_r(f) = [M(|f|^r]^{1/r}$      34 157Ч158 219 222 422
Maximal functions, bounds independence of dimension      523Ч525
Maximal functions, comparison of $M_{\Phi}$, $M_{\Phi}^{\ast}$, $\mathcal{M}_{\mathcal{F}}$      92Ч101\
Maximal functions, comparison of M, $M^{\Delta}$      188
Maximal functions, dyadic $M^{\Delta}$      149Ч151 153Ч155 202Ч203 213
Maximal functions, grand $\mathcal{M}_{\mathcal{F}}$      90 99Ч100 146
Maximal functions, homogeneous $M_{\Omega}$      72 83
Maximal functions, linearization      29 49 317Ч318
Maximal functions, martingale      187 223
Maximal functions, nontangential $u^{ast}$, $M_{\Phi}^{\ast}$      56Ч57 62 90 92 184
Maximal functions, sharp bounds      42
Maximal functions, spherical averages of      466
Maximal functions, strong Ms      83Ч85 446Ч447 458 462
Maximal functions, tangential      79 92
Maximal functions, usual M      3 9 16 354 474 478
Maximal functions, vector-valued      50Ч56 75Ч76 80 463
Maximal functions, vertical $u^+$, $M_{\Phi}$      69Ч70 90
Maximal functions, weak-type principle      441Ч444 456Ч458
Mehler kernel      582 583
Metaplectic representation      578
Method of descent      see УLifting techniqueФ
Method of rotations      72
Molecules      130
Moment conditions      87 99 104Ч106 128 129
MorseТs Lemma      346
Multilinear operators      326Ч328
Multipliers and linear subspaces      515
Multipliers ball      389 450Ч454
Multipliers for singular integrals      24Ч26 245Ч249 262Ч263
Multipliers on $H^n$      642
Multipliers, half-line      452
Multipliers, half-space      450
Multipliers, Marcinkiewicz      26 174 263 464
Nikodym set      455
Nilpotent groups      517 635
Nilpotent groups, free      637 640Ч641
Nilpotent groups, Lie algebras      621 635
Nonmeasurable sets      70 77
One-parameter groups      584
One-parameter groups and dilations      637
Orlicz spaces      43 84 128 458 526
Ornstein Ч Uhlenbeck process      582 642
Orthogonality      278Ч288
Orthogonality and BMO      166Ч173
Orthogonality and singular integrals      295Ч300
Orthogonality on homogeneous groups      623Ч627
Orthogonality, almost      257 269Ч270 278
Orthogonality, lack of      272Ч273
Orthogonality, method of $TT^{\ast}$      278Ч279 317Ч318 353 364 378 381 398 400 431
Oscillatory integrals      3 5 329Ч347 375Ч386 414Ч418
Oscillatory integrals and $H^n$      581
Oscillatory integrals and Fourier transform      378
Oscillatory integrals in $\mathbb{R}^2$      412Ч414
Oscillatory integrals on $L^2$      377Ч383 500Ч501
Oscillatory integrals on $L^p$      379Ч386 392Ч393 412Ч414
Oscillatory integrals, adjoints      378Ч381
Oscillatory integrals, asymptotics      334Ч341 355Ч360
Oscillatory integrals, endpoint contributions      331 355
Oscillatory integrals, finite-type phase      416
Oscillatory integrals, localization      330 341 396
Oscillatory integrals, scaling      332 342
Oscillatory integrals, sharp exponents      412 417Ч418
Oscillatory integrals, singular phase      415
Oscillatory singular integrals      373 416Ч417 423 557Ч561
Oscillatory singular integrals on $L^1$      431
Parametrix      241 266
Paraproducts      274 302Ч305 326Ч328
Phase functions      330 377 380 427
Phase functions and Gaussian curvature      360 (see also УHessian determinantФ)
Phase functions and rotational curvature      517
Phase functions, duality      358
Phase functions, extension      381
Phase functions, Newton diagram      359
Phase functions, nondegeneracy      394
Phase functions, oscillatory index      359
Phase functions, polynomial      416
Phase functions, rank      363
Poisson integrals and BMO      165
Poisson integrals on $\mathbb{R}^n$      3 90
Poisson integrals on symmetric spaces      71 78 82 85 447Ч449 458Ч459 637 638
Poisson kernel      24 47 89 99
Poisson kernel for $\square^{\tau}$      629
Poisson kernel, conjugate      121
Poisson summation formula      362
Principal type      321
Product theory of $\mathbb{R}^n$      83Ч85 138 446Ч447
Pseudo-differential operators      5 228Ч288
Pseudo-differential operators and Fourier integral operators      395 402Ч403
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