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Guy David — Wavelets and Singular Integrals on Curves and Surfaces
Guy David — Wavelets and Singular Integrals on Curves and Surfaces

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Название: Wavelets and Singular Integrals on Curves and Surfaces

Автор: Guy David

Аннотация:

Wavelets are a recently developed tool for the analysis and synthesis of functions; their simplicity, versatility and precision makes them valuable in many branches of applied mathematics. The book begins with an introduction to the theory of wavelets and limits itself to the detailed construction of various orthonormal bases of wavelets. A second part centers on a criterion for the L2-boundedness of singular integral operators: the T(b)-theorem. It contains a full proof of that theorem. It contains a full proof of that theorem, and a few of the most striking applications (mostly to the Cauchy integral). The third part is a survey of recent attempts to understand the geometry of subsets of Rn on which analogues of the Cauchy kernel define bounded operators. The book was conceived for a graduate student, or researcher, with a primary interest in analysis (and preferably some knowledge of harmonic analysis and seeking an understanding of some of the new "real-variable methods" used in harmonic analysis.


Язык: en

Рубрика: Математика/

Серия: Lecture Notes in Mathematics

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 107

Добавлена в каталог: 28.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$H^{1}$ (Hardy space)      24 49
$L^{p}$-boundedness      28 49
$\omega$-regular surface      71 77 88 98
Ahlfors-regular curve      64 88
Besicovitch-regular(rectifiable)      63 89
Big disks surfaces      78 97
Big pieces      62 63 64 72 76 86 88 91 97
Big projections      77 79 86 91 92 97
Bilipschitz mappings      62 79 88 97
BMO      25 28 30 31 44 70
Calderon commutators      50
Calderon reproducing formula      1
Calderon — Zygmund operator      28
Calderon's theorem      50
Carleson measure      33 44 84 88
Cauchy integral      50 66 67 91 99
Chord-arc curve      51
Chord-arc surface      69 89 97
Clifford algebra      73 83 90
Coifman, McIntosh and Meyer's theorem      50 51 60
Corona construction      86 88
Cotlar inequality      59
Daubechies' compacdy supported wavelets      15
Dyadic cubes      48 74 86 93
Garnett's counterexample      51 67
Geometric lemma      84 88 99
Good $\lambda$ inequalities      60
Good kernel      55
Gram orthogonalisation      6
Grochenig — Meyer construction      12
Haar system      2 10 12
Harmonic measure      78 97
Hausdorff measure      62
Homogeneous type (space of)      47
Jones' traveling salesman theorem      85 89
Lipschitz graphs      50 53 59 66 84 88 97
Maximal function      58
Maximal operator      28 56
Meyer's wavelet      10
Multiscale analysis      2
Paraaccretive function      30
Parametrizations      89
Paraproduct      44
Principal values      27 30 63
Quasiconformal, quasisymmetric      72 89 90
Rectifiable set      63 89
Regularity (of a MSA)      4
Rising Sun Lemma      65
Rotation method      54
Semmes surface      72 77 7 8 97
Shur's lemma      43
Singular integral operator      26
Sobolev inequalities      90 97
Space of homogeneous type      47
Spline functions      3 5 10
Square function estimates      33 83 88 98
Stable kernel      52
Standard kernel      26
Strong $A_{\infty}$ weight      90
T(1)      27 30
T(b)      31 73
Tensor product (of MSA’s)      5 11
Traveling salesman      85 89
Weak boundedness      29 40
Weak geometric lemma      85 97
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