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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
$A_2$      194 216—217 225—226
$A_p$ weights      193—227
$A_u$      56 197 214—216
$A_{\infty}$      196 201—203 212—214 218 219 225
$A_{\infty}$ and BMO      141 177 197 218 219 225
$A_{\infty}$ and maximal functions      195 198—203
$A_{\infty}$ and real-variable structures      223
$A_{\infty}$ and singular integrals      204—211 221
$A_{\infty}$, $ML^p(\omega)$      210 222
$A_{\infty}$, duality      194
$A_{\infty}$, extrapolation theorem      223
$A_{\infty}$, factorization      216—217
$A_{\infty}$, functions in      218
$A_{\infty}$, interpolation      218
$A_{\infty}$, overspill      202 212—214 218
$A_{\infty}$, relative      219 (see also “Severse Holder inequalities”)
$F^{p,q}_{\gamma}$ (Triebel — Lizorkin spaces)      264 319
$H^1$      88 91—92 128
$H^1$ and BMO      142—144 163—165 178 183
$H^1$ and Fourier integral operators      402—405 410—411 428
$H^1$ and VMO      180
$H^1$, atomic decomposition      77 142 147
$H^1$, atoms      91 129
$H^1$, dense subspace $H^1_{\alpha}$      142
$H^1$, functions in      137 178
$H^1$, martingale      188 (see also “Singular integrals”)
$H^n$ (Heisenberg group)      5 11 517 527—588 594—618 627—635
$H^n$ (Heisenberg group) and rotational curvature      495
$H^n$ (Heisenberg group) as translations of $\mathcal{U}^n$      530
$H^n$ (Heisenberg group), approximation by      631 639—640
$H^n$ (Heisenberg group), balls $B(x,\delta)$      542
$H^n$ (Heisenberg group), dilations      541
$H^n$ (Heisenberg group), Fourier transform      569—573 583
$H^n$ (Heisenberg group), Haar measure      531
$H^n$ (Heisenberg group), heat equation      632—633 642—643
$H^n$ (Heisenberg group), Lie algebra $h^n$      543—547 584
$H^n$ (Heisenberg group), multiplication law      530
$H^n$ (Heisenberg group), multipliers      642
$H^n$ (Heisenberg group), nonstandard dilations      620
$H^n$ (Heisenberg group), norm $\rho$      541 638
$H^n$ (Heisenberg group), polar coordinates      542
$H^n$ (Heisenberg group), radial functions      583
$H^n$ (Heisenberg group), representations      551 568—569 577 598 635
$H^n$ (Heisenberg group), restriction theorems      642
$H^n$ (Heisenberg group), Riesz transforms      605—608
$H^n$ (Heisenberg group), singular integrals      536—543 557—568 580—581 586
$H^n$ (Heisenberg group), vector fields X, Y, Z, T      544—547 584 597 598
$H^p$ (Hardy spaces)      4 87—138
$H^p$ (Hardy spaces) and $L^p$      87 91 92
$H^p$ (Hardy spaces) and $M_{\Phi}$ ($\Phi$ singular)      130—131
$H^p$ (Hardy spaces) and Fourier transform      128
$H^p$ (Hardy spaces) and harmonic functions      88 118—127 133—134
$H^p$ (Hardy spaces) and real-variable structures      186 (see also “Singular integrals”)
$H^p$ (Hardy spaces) and weights      223
$H^p$ (Hardy spaces), atomic decomposition      105—112 137 182
$H^p$ (Hardy spaces), atoms      105—106 112 130
$H^p$ (Hardy spaces), boundary values      127
$H^p$ (Hardy spaces), definitions      87
$H^p$ (Hardy spaces), dense subspaces      109—112 128 133
$H^p$ (Hardy spaces), distributions in      88 129 131
$H^p$ (Hardy spaces), duals for p < 1      130
$H^p$ (Hardy spaces), maximal characterization      90—101 131
$H^p$ (Hardy spaces), norm $|| ||_{H^p}$      100
$H^p$ (Hardy spaces), product theory      138
$H^p$ (Hardy spaces), topology      100 127
$H^p_{loc}$ (local $H^p$)      134 264
$H^p_{loc}$ (local $H^p$), distributions in      135—136 429
$l^p$      4 13
$L^p_k$ (Sobolev spaces)      251—252 634
$L^p_k$ and $F^{p,q}_{\gamma}$      264
$L^p_k$ and $L^{p,q}$      265
$L^p_k$ and $\Lambda^{p,q}_{\gamma}$      264
$L^p_k$ and tangential approach      79
$L^p_k$, nonisotropic $NL^p_k$      606—610 634
$L^{p,q}$ (Lorentz spaces)      36 265 418 526
$NL^p_k$      see “$L^p_k$”
$S^m$ (usual symbols)      229 232—263
$S^m$ (usual symbols) and BMO      264
$S^m$ (usual symbols) and singular integrals      235 241—249
$S^m$ (usual symbols) on $H^1$      402—403
$S^m$ (usual symbols) on $H^p$      264
$S^m$ (usual symbols) on $L^2$      234—237
$S^m$ (usual symbols) on $L^p$      250
$S^m$ (usual symbols) on $L^p_k$      251—252 (see also “Pseudo-differential operators”)
$S^m$ (usual symbols) on $\Lambda_{\gamma}$      253—257
$S^m$ (usual symbols) on S      232
$S^m$ (usual symbols), $S^{-\infty}$      261
$S^m$ (usual symbols), adjoints      259 554
$S^m$ (usual symbols), calculus      237—241 579
$S^m$ (usual symbols), change of variables      259
$S^m$ (usual symbols), commutators      261 308—312
$S^m$ (usual symbols), dyadic decomposition      243—245 253—257
$S^m$ (usual symbols), homogeneity      262
$S^m$ (usual symbols), kernels      235 241—245 262
$S^m$ (usual symbols), symmetric $S^m_{sym}$      579
$S^m_{1,1}$ (forbidden symbols)      270—275
$S^m_{1,1}$ (forbidden symbols) and singular integrals      269 302 324
$S^m_{1,1}$ (forbidden symbols) on $L^2$      272—273
$S^m_{1,1}$ (forbidden symbols) on $L^p_k$      319
$S^m_{1,1}$ (forbidden symbols) on $\Lambda_{\gamma}$      274—275
$S^m_{1,1}$ (forbidden symbols), dyadic decomposition      271—275
$S^m_{1,1}$ (forbidden symbols), kernels      271
$S^m_{\rho,\delta}$ (exotic symbols)      271
$S^m_{\rho,\delta}$ (exotic symbols) on $L^2$      319
$S^m_{\rho,\delta}$ (exotic symbols) on $L^p$      322—323
$S^m_{\rho,\delta}$ (exotic symbols) on S      271
$S^m_{\rho,\delta}$ (exotic symbols), calculus      320
$S^m_{\rho,\delta}$ (exotic symbols), examples      277—278
$S^m_{\rho,\delta}$ (exotic symbols), frequency decomposition      319
$S^m_{\rho,\rho}$ (exotic symbols)      276 282—288
$S^m_{\rho,\rho}$ (exotic symbols) on $L^2$      282—288 323
$S^m_{\rho,\rho}$ (exotic symbols) on $L^p_k$      319
$S^m_{\rho,\rho}$ (exotic symbols), dyadic decomposition      286—288
$S^m_{\rho,\rho}$ (exotic symbols), examples      276—277 585—586
$S^m_{\rho,\rho}$ (exotic symbols), frequency decomposition      282—285
$S^{M,m}_{\Phi,\phi}$      320—321
$T_a$ (operator w/symbol a)      231
$\bar{\partial}$-complex      591—592
$\bar{\partial}$-Neumann problem      587 592 627—631
$\bar{\partial}$-Neumann problem and integral formulas      631
$\bar{\partial}$-Neumann problem and strong pseudoconvexity      631
$\bar{\partial}$-Neumann problem and weak pseudoconvexity      631
$\bar{\partial}$-Neumann problem, sharp estimates      631
$\bar{\partial}$-Neumann problem, solution on $\mathcal{U}^n$      630
$\bar{\partial}_b$-complex      592—595
$\Lambda_{\gamma}$ (Lipschitz spaces)      130 253—257 274
$\Lambda_{\gamma}$ (Lipschitz spaces), $\Lambda^{p,q}_{\gamma}$      264 319
$\Lambda_{\gamma}$ (Lipschitz spaces), nonisotropic $\Gamma_{\gamma}$ (Lipschitz spaces)      634
$\mathcal{H}^p$ (holomorphic $H^p$)      131—132 137 226
$\mathcal{H}^p$ (holomorphic $H^p$), $\mathcal{H}^2($\mathcal{U}^n$)$      532—541
$\mathcal{H}^p$ (holomorphic $H^p$), boundary values      532—535
$\mathcal{N}$ (tent spaces)      58—65 77—78
$\mathcal{N}$ (tent spaces) and Carleson measures      59—61 63 77 161—163
$\mathcal{N}$ (tent spaces), $\mathcal{N}^2$      161—164
$\mathcal{N}$ (tent spaces), $\mathcal{N}^p_r$      180—184
$\mathcal{N}$ (tent spaces), atomic decomposition      63—65 77 181—182
$\mathcal{N}$ (tent spaces), atoms      63 181
$\mathcal{S}$ (Schwartz class)      88
$\mathcal{S}'$ (tempered distributions)      89
$\mathcal{S}_{\mathcal{F}}$      90
$\mathcal{U}^n$ (upper half-space)      528—543 587
$\mathcal{U}^n$ (upper half-space), $b\mathcal{U}^n$ (boundary)      529 545—547 641—642
$\mathcal{U}^n$ (upper half-space), $\bar{\partial}$-Neumann problem      627—631
$\mathcal{U}^n$ (upper half-space), $\mathcal{H}^2(\mathcal{U}^n)$      532—541
$\mathcal{U}^n$ (upper half-space), automorphism group      574—576
$\mathcal{U}^n$ (upper half-space), coordinates $[\zeta,t, r]$      531 628
$\mathcal{U}^n$ (upper half-space), defining function r(z)      530
$\mathcal{U}^n$ (upper half-space), dilations      530 538
$\mathcal{U}^n$ (upper half-space), equivalence with ball      529
$\mathcal{U}^n$ (upper half-space), measure $d\beta$      532
$\mathcal{U}^n$ (upper half-space), rotations      530
$\mathcal{U}^n$ (upper half-space), translation group $H^n$      530
$\mathfral{L}$ (sub-Laplacian)      39 46 636 642
$\mathfral{L}_{\alpha}$      588 596—610 628—630 632—635
$\mathfral{L}_{\alpha}$, forbidden values      598
$\mathfral{L}_{\alpha}$, fundamental solution $F_{\alpha}$      598—602 632
$\mathfral{L}_{\alpha}$, hypoellipticity      604 635
$\mathfral{L}_{\alpha}$, invertibility      598 635
$\mathfral{L}_{\alpha}$, local solvability      602—604
$\mathfral{L}_{\alpha}$, relative solution      615—618 634
$\mathfral{L}_{\alpha}$, sharp regularity      609—610
$\mathfral{L}_{\alpha}$, solution operator $S_{\alpha}$      602
$\mathfral{L}_{\alpha}$, symmetry      596 599 633—634
$\zeta$-convexity      48
a(x, D) (operator w/symbol a)      231
Approximations of the identity      23—24 56 198 242
Approximations of the identity and singular integrals      81
Approximations of the identity, relations between      93—94 138
Approximations of the identity, singular      71—75 80—83 130—131 481
Approximations of the identityon homogeneous groups      638
Area integral      47 182—184
Area integral and $H^p$      124—127
Atomic decomposition in $H^1$      77 142 147
Atomic decomposition in $H^p$      105—112 137 182
Atomic decomposition in $L^1$      129
Atomic decomposition in $L^p$ (p > 1)      112 185
Atomic decomposition in $N^p$      181—182
Atomic decomposition in N      63—65 77
Atomic decomposition, localized      137
Atoms in $H^1$      91 129
Atoms in $H^p$      105—106 112 130
Atoms in $N^p$      181
Atoms in N      63
Averages over hypersurfaces      467—472 493—511 517—525
Averages over hypersurfaces and $L^p_k$      370—372 517
Averages over hypersurfaces and averages over submanifolds      467—469
Averages over hypersurfaces and Fourier integral operators      360 496 517
Averages over hypersurfaces in $\mathbb{R}^2$      519—523
Averages over hypersurfaces on $L^1$      503
Averages over hypersurfaces, $L^2$ estimates      469—471 501—502 504—507
Averages over hypersurfaces, $L^p$ estimates      370—372 471—472 499 503 507
Averages over hypersurfaces, curvature has zeros      512 518
Averages over hypersurfaces, definability on $L^p$      508—509
Averages over hypersurfaces, dilated      510—511
Averages over hypersurfaces, dimension restrictions      471—472 502 509—510
Averages over hypersurfaces, finite type      518
Averages over hypersurfaces, sharp exponents      471—472
Averages over hypersurfaces, smoothing      173—174 370—372 517
Averages over hypersurfaces, spheres      131 173—174 395 399 469—472 518—519 523
Averages over hypersurfaces, variable      493—499
Averages over measures on universal variety      486—489
Averages over measures, $L^2$ estimates      487—488 511
Averages over measures, $L^p$ estimates      486—489 514
Averages over measures, cancellation conditions      513
Averages over measures, Fourier transform      486 513
Averages over measures, lifting technique      483—486
Averages over rectangles and averages over hypersurfaces      467—469
Averages over rectangles and real-variable structures      473 478
Averages over rectangles and singular Radon transforms      513—517
Averages over rectangles, $L^1$ estimates      526
Averages over rectangles, $L^2$ estimates      472—476 478—479
Averages over rectangles, $L^p$ estimates      476—482 485—486 490—493
Averages over rectangles, algebraic varieties      477 485—486
Averages over rectangles, angles and bounds      464—466
Averages over rectangles, arbitrary orientations      445—446 449 455
Averages over rectangles, convex      525—526
Averages over rectangles, definability on $L^p$      492—493
Averages over rectangles, eccentricity and bounds      419 464—466
Averages over rectangles, finite type      476—477 490—493
Averages over rectangles, infinitely flat      493 512—513 525—526
Averages over rectangles, lacunary orientations      459—464
Averages over rectangles, on $L^1$      493
Averages over rectangles, parabola      472—476
Averages over rectangles, singularities      493
Averages over rectangles, universal variety      477—482
Averages over rectangles, unrotated      83—85 446—447 458
Averages over rectangles, variable      516—517
Averages over submanifolds      467—469 472—493 512—517
Balls      8—9
Balls, equivalence      10
Balls, examples      9—12 37—39 41 361 473 478 542 620
Besicovitch set      433—440 445 453—456 510
Besicovitch set, higher-dimensional analogues      455
Bessel functions      131 338 347 356—357 390 395 426 430
BMO (bounded mean oscillation)      139—180 300—305
BMO (bounded mean oscillation) and $A_p$      141 177 197 218 219 225
BMO (bounded mean oscillation) and $H^1$      142—144 163—165 178 183
BMO (bounded mean oscillation) and Carleson measures      158—173 180—184 303
BMO (bounded mean oscillation) and Fourier integral operators      411 427
BMO (bounded mean oscillation) and harmonic functions      165
BMO (bounded mean oscillation) and homeomorphisms of $\mathbb{R}^n$      180 219
BMO (bounded mean oscillation) and square functions      158—173 180—184
BMO (bounded mean oscillation), distance to $L^{\infty}$      180 186
BMO (bounded mean oscillation), dyadic      154 173
BMO (bounded mean oscillation), functions in      140—141 177—179
BMO (bounded mean oscillation), local      264
BMO (bounded mean oscillation), martingale      188
BMO (bounded mean oscillation), orthogonal expansions      166—173 (see also “Singular integrals”)
BMO (bounded mean oscillation), weak topology      166 186 301
Bochner — Riesz means      388—394 418—423
Bochner — Riesz means and $H^p$      131
Bochner — Riesz means and restriction theorems      422
Bochner — Riesz means in $\mathbb{R}^2$      412—414 418—420
Bochner — Riesz means in $\mathbb{R}^n$, n > 3      423
Bochner — Riesz means on compact manifolds      431
Bochner — Riesz means, analogue for cones      521
Bochner — Riesz means, kernel      390 430
Bochner — Riesz means, maximal      420—423
Bochner — Riesz means, sharp exponents      389 414 430
Bounded distribution      89
Bounds independent of dimension      523—525
Brownian motion      189 642—643
Bump functions      293
Bump functions and $S^m$      262
Bump functions and $\mathcal{M}_F$      100 (see also “Restricted boundedness”)
Bump functions and BMO      300—301
Bump functions and singular integrals      248—249 293—295
Calderon — Zygmund decomposition      16—18 20 51 101—105 110 138 150 431
Calderon — Zygmund kernels      289 305
Calderon — Zygmund operators      191 325
Calderon — Zygmund, symbolic calculus      268
Campbell — Hausdorff formula      584 635
Cancellation conditions      26 248 562 622
Cancellation conditions and averages over measures      513
Cancellation conditions for $S^m$      262
Cancellation conditions for atoms      see “Moment conditions”
Cancellation conditions, necessity      289—292 305—308
Cancellation conditions, special $T1 = T^{\ast}l = 0$      295 299 624
Cancellation conditions, sufficiency      305—308\
Canonical coordinates      584 636
Canonical transformations      396
Carleman estimates      370
Carleson measures      58—59 78 314
Carleson measures and $\mathcal{N}$      59—61 63 77 161—163
Carleson measures and BMO      158—173 180—184 303
Carleson measures and weights      225
Carleson measures, operator $\mathfrak{T}$      162—163 181—183
Carleson measures, space $\mathcal{C}$      59
Cauchy integral      310—316
Cauchy — Riemann operators      589—592
Cauchy — Riemann operators, tangential      545—547 592—593
Cauchy — Szego projection      5 532—543
Cauchy — Szego projection and $\mathfrak{L}_{\alpha}$      601 615—618
Cauchy — Szego projection and Lewy example      611—618
Cauchy — Szego projection on $L^2$      537
Cauchy — Szego projection on $L^p$      541—543
Cauchy — Szego projection, Fourier transform      573
Cauchy — Szego projection, kernel      277 536—541 575—577 580 585 601
Characteristic polynomial      231
Commutation relations      545 546 548—549 593
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