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



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

Àâòîð: Stein E.M.

ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/Àíàëèç/Ïðîäâèíóòûé àíàëèç/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1993

Êîëè÷åñòâî ñòðàíèö: 695

Äîáàâëåíà â êàòàëîã: 02.04.2005

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Commutators      179
Commutators, Calderon      308—312 324
Compensated compactness      137
cones      58 132 447—449 461
Cones and spheres      459
Cones, aperture      58 62 93 124—127 183—184
Conjugate functions and $H^p$      120—123 133
Continuity in measure      456—458
Cotlar’s lemma      279—282 318
Cotlar’s lemma for integrals      318
Covering lemmas      4 84 465
Covering lemmas, Besicovitch      44
Covering lemmas, Borel — Cantelli      442—443
Covering lemmas, Vitali      8 12 84
Covering lemmas, Whitney decomposition      14—17 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      467—469
Curvature and Fourier transforms      330
Curvature, cinematic      519—520 (see also “Finite type”)
Curvature, Gaussian      348 351 360—363 494—497
Curvature, principal      348 351 360—361 365
Curvature, rotational      494—497 500 517
Curvature, total      348
Differentiation of integrals      13 44 65 433 441 455
Differentiation of integrals over hypersurfaces      469 509
Differentiation of integrals over submanifolds      492—493
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      24 223—225 590 629
Dirichlet problem for $\bar{\partial}$      641—642
Distance      see “Quasi-distance”
Distributional inequalities      23 69 151—155 184 188 206—209
Doubling measures      8 12 39—41 151 196 218
Doubling measures and Zygmund condition      225
Duality, $H^1$ and BMO      142—144 163—165 178 183
Duality, $H^p$ and $\Lambda_{\gamma}$      130
Duality, $\mathcal{N}$ and $\mathcal{C}$      59—61 63 77 161—163
Duality, $\mathcal{N}^p$ and $\mathcal{N}^q$      181
Duality, inequalities      59 146—147 161—163
Duality, VMO and $H^1$      180
Dyadic cubes      149
Dyadic decomposition      241—243 253—257 403
Dyadic decomposition and square functions      267
Dyadic decomposition for $S^m$      243—245 253—257
Dyadic decomposition for $S^m_{1,1}$      271—275
Dyadic decomposition for singular integrals      246—247 295—296
Dyadic decomposition in $\mathbb{R}^1$      501 506
Dyadic decomposition, nondyadic decompositions      282—285 319
Dyadic decomposition, second      403—406 419 522—523
Eikonal equation      425
Elliptic operators      230—231 241 266
Elliptic operators and weights      223—225
entropy      83
Euclidean balls      9
Euclidean measure      9
Exponential integrability      144—146 154—155 184
Exponential sums      373
Fatou theorem      119—120 133
Finite type      350—351
Finite type and vector fields      516
Fourier integral operators      173 375—376 394—412 424—429
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      399—401 428—429
Fourier integral operators and pseudo-differential operators      395 402—403
Fourier integral operators in $\mathbb{R}^1$      430
Fourier integral operators in $\mathbb{R}^2$      519—523
Fourier integral operators on $H^1$      402—405 410—411 428
Fourier integral operators on $L^2$      397—398
Fourier integral operators on $L^p$      399 402 410—412
Fourier integral operators on $L^p_k$      429
Fourier integral operators on $L^{\infty}$      411 (see also “Phase functions”)
Fourier integral operators on $\Lambda_{\gamma}$      429
Fourier integral operators, adjoints      400 410
Fourier integral operators, examples      394—396
Fourier integral operators, extended      424—425
Fourier integral operators, frequency decomposition      403—410
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      372—373
Fourier transform of surface-carried measure, sphere      174 347—348
Fourier transform of surface-carried measure, unbounded      363—364
Fourier transform of surface-carried measures      347—351 360—364
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      362—363
Fourier transform of surface-carried measures and principal curvatures      360—361 365
Fourier transform of surface-carried measures and real-variable structures      361 (see also “Restriction theorems”)
Fourier transform of surface-carried measures, curvature has zeros      360—362
Fourier transform of surface-carried measures, curved hypersurfaces      348—350 360
Fourier transform of surface-carried measures, finite type      350—351 353 475 479 492
Fourier transform of surface-carried measures, homogeneous      363—364
Fourier transform of surface-carried measures, hyperplanes      351
Fourier transform of surface-carried measures, measure in $L^p(d\sigma)$      372—373
Fourier transform of surface-carried measures, real analytic      361
Fourier transform on $H^n$      569—573
Fourier transform, convergence      388—390 423
Fourier transform, measures of bounded variation      420 (see also “Multipliers”)
Fourier transform, nondyadic decompositions      282—285 319
Fourier transform, radial functions      430
Fractional integration      353—354 414
Fractional integration and $H^p$      136
Fractional integration and BMO      178
Fractional integration and Fourier integral operators      399—401 428—429
Fractional integration and real-variable structures      45
Fractional integration on $L^{p,q}$      265
Fractional integration, imaginary order      33 46
Freeing of monomials      see “Lifting technique”
Freezing principle      230—231
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      312—316
Hardy — Littlewood — Sobolev theorem      see “Fractional integration”
Harmonic measure      41 224—225
Hausdorff — Young inequality      583
Heat equation      24 276
Heat equation on $H^n$      632—633 642—643
Helson — Szego theorem      225—227
Hermite expansions      571—573 582—584
Hermite operator      549 571 579 598
Hessian determinant      377 384
Hessian determinant and rotational curvature      496
Hessian determinant, zeros      412 415
Hilbert transform      3 26 225—227 389 424
Hilbert transform and Cauchy integral      311
Hilbert — Schmidt class      554—556 570—571
Hilbert — Schmidt norm      415
Homogeneous dimension      478 620 638
Homogeneous distributions      45 262—263
Homogeneous groups      11 83 186 618—627 635—641
Homogeneous groups, balls $B(x,\delta)$      620
Homogeneous groups, dilations      618 621 637
Homogeneous groups, examples      620—621
Homogeneous groups, Haar measure      619
Homogeneous groups, Lie algebras      621—622 635—637
Homogeneous groups, lifting technique      639—641
Homogeneous groups, maximal functions      638
Homogeneous groups, nilpotence      621
Homogeneous groups, norm $\rho$      619 638
Homogeneous groups, singular integrals      622—627
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      173—177
Interpolation of operators, averaging operators      371
Interpolation of operators, complex $L^p$      384—385
Interpolation of operators, Fourier integral operators      410—412
Interpolation of operators, Fourier restriction      352 365
Interpolation of operators, Marcinkiewicz      14 22 36 265 465
Interpolation of operators, maximal averages      14 479—482 487—489 503 507 518—519
Interpolation of operators, oscillatory integrals      381—386
Interpolation of operators, singular integrals      22 36 514
Iwasawa decomposition      621 637
John — Nirenberg inequality      144—146 154—155 179
Jump theorem      580
Kakeya needle problem      434 454—455
Klein — Gordon equation      372
Kohn Laplacian $\square_b$      592—593 596—597
Kohn Laplacian $\square_b$ on functions      615—618
Kohn Laplacian $\square_b$ on pseudoconvex domains      639
Lagrangian distributions      429
Laguerre functions      584
Laplace — Beltrami operator      431
Laplacian $(\Delta,\square)$      24 590 592 629
Lattice points, distribution      362
Layer potentials      224
Levi form      593
Lewy operator      611—618
Lewy operator, unsolvable equations      612—615
Lifting technique      468 513—517
Lifting technique and homogeneous groups      639—641
Lifting technique, freeing of monomials      477—478
Lifting technique, method of descent      483—486 490—491
Lifting technique, universal variety      477—478
Lipschitz domains      137 223—225 310—316
Littlewood — Paley decomposition      see “Dyadic decomposition”
LlogL      see “Orlicz spaces”
Local smoothing      521—523
Local solvability      604 611
Marcinkiewicz integral      76
Martingales      151 187—190
Martingales and real-variable structures      189
Martingales, dyadic      187
Maximal functions      3 7—14 49—75 87—101 433—434 440—449 455—511
Maximal functions and balls $M_B$      65—69 78—79
Maximal functions and sets $M_C$      433 441
Maximal functions and singular integrals      34—36 157—158
Maximal functions and weights      195 198—203
Maximal functions on $H^p$      87—112
Maximal functions on $L^1$      13—14 43 51—53 72 84 446 458
Maximal functions on $L^2$      317—318
Maximal functions on $L^p$      441 445
Maximal functions on BMO      179
Maximal functions on homogeneous groups      638
Maximal functions, $M_r(f) = [M(|f|^r]^{1/r}$      34 157—158 219 222 422
Maximal functions, bounds independence of dimension      523—525
Maximal functions, comparison of $M_{\Phi}$, $M_{\Phi}^{\ast}$, $\mathcal{M}_{\mathcal{F}}$      92—101\
Maximal functions, comparison of M, $M^{\Delta}$      188
Maximal functions, dyadic $M^{\Delta}$      149—151 153—155 202—203 213
Maximal functions, grand $\mathcal{M}_{\mathcal{F}}$      90 99—100 146
Maximal functions, homogeneous $M_{\Omega}$      72 83
Maximal functions, linearization      29 49 317—318
Maximal functions, martingale      187 223
Maximal functions, nontangential $u^{ast}$, $M_{\Phi}^{\ast}$      56—57 62 90 92 184
Maximal functions, sharp bounds      42
Maximal functions, spherical averages of      466
Maximal functions, strong Ms      83—85 446—447 458 462
Maximal functions, tangential      79 92
Maximal functions, usual M      3 9 16 354 474 478
Maximal functions, vector-valued      50—56 75—76 80 463
Maximal functions, vertical $u^+$, $M_{\Phi}$      69—70 90
Maximal functions, weak-type principle      441—444 456—458
Mehler kernel      582 583
Metaplectic representation      578
Method of descent      see “Lifting technique”
Method of rotations      72
Molecules      130
Moment conditions      87 99 104—106 128 129
Morse’s Lemma      346
Multilinear operators      326—328
Multipliers and linear subspaces      515
Multipliers ball      389 450—454
Multipliers for singular integrals      24—26 245—249 262—263
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      637 640—641
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 — Uhlenbeck process      582 642
Orthogonality      278—288
Orthogonality and BMO      166—173
Orthogonality and singular integrals      295—300
Orthogonality on homogeneous groups      623—627
Orthogonality, almost      257 269—270 278
Orthogonality, lack of      272—273
Orthogonality, method of $TT^{\ast}$      278—279 317—318 353 364 378 381 398 400 431
Oscillatory integrals      3 5 329—347 375—386 414—418
Oscillatory integrals and $H^n$      581
Oscillatory integrals and Fourier transform      378
Oscillatory integrals in $\mathbb{R}^2$      412—414
Oscillatory integrals on $L^2$      377—383 500—501
Oscillatory integrals on $L^p$      379—386 392—393 412—414
Oscillatory integrals, adjoints      378—381
Oscillatory integrals, asymptotics      334—341 355—360
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      412 417—418
Oscillatory integrals, singular phase      415
Oscillatory singular integrals      373 416—417 423 557—561
Oscillatory singular integrals on $L^1$      431
Parametrix      241 266
Paraproducts      274 302—305 326—328
Phase functions      330 377 380 427
Phase functions and Gaussian curvature      360 (see also “Hessian determinant”)
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 85 447—449 458—459 637 638
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 $\mathbb{R}^n$      83—85 138 446—447
Pseudo-differential operators      5 228—288
Pseudo-differential operators and Fourier integral operators      395 402—403
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