| Translator's note | p. x |
| Preface to the English edition | p. xi |
| Introduction | p. xiii |
| Introduction to Wavelets and Operators | p. xv |
| The new Calderon-Zygmund operators | |
| Introduction | p. 1 |
| Definition of Calderon-Zygmund operators corresponding to singular integrals | p. 8 |
| Calderon-Zygmund operators and L[superscript p] spaces | p. 13 |
| The conditions T(1) = 0 and [superscript t]T(1) = 0 for a Calderon-Zygmund operator | p. 22 |
| Pointwise estimates for Calderon-Zygmund operators | p. 24 |
| Calderon-Zygmund operators and singular integrals | p. 30 |
| A more detailed version of Cotlar's inequality | p. 34 |
| The good [lambda] inequalities and the Muckenhoupt weights | p. 37 |
| Notes and additional remarks | p. 41 |
| David and Journe's T(1) theorem | |
| Introduction | p. 43 |
| Statement of the T(1) theorem | p. 45 |
| The wavelet proof of the T(1) theorem | p. 51 |
| Schur's lemma | p. 54 |
| Wavelets and Vaguelets | p. 56 |
| Pseudo-products and the rest of the proof of the T(1) theorem | p. 57 |
| Cotlar and Stein's lemma and the second proof of David and Journe's theorem | p. 60 |
| Other formulations of the T(1) theorem | p. 64 |
| Banach algebras of Calderon-Zygmund operators | p. 65 |
| Banach spaces of Calderon-Zygmund operators | p. 71 |
| Variations on the pseudo-product | p. 73 |
| Additional remarks | p. 76 |
| Examples of Calderon-Zygmund operators | |
| Introduction | p. 77 |
| Pseudo-differential operators and Calderon-Zygmund operators | p. 79 |
| Commutators and Calderon's improved pseudo-differential calculus | p. 89 |
| The pseudo-differential version of Leibniz's rule | p. 93 |
| Higher order commutators | p. 96 |
| Takafumi Murai's proof that the Cauchy kernel is L[superscript 2] continuous | p. 98 |
| The Calderon-Zygmund method of rotations | p. 105 |
| Operators corresponding to singular integrals: their continuity on Holder and Sobolev spaces | |
| Introduction | p. 111 |
| Statement of the theorems | p. 112 |
| Examples | p. 114 |
| Continuity of T on homogeneous Holder spaces | p. 117 |
| Continuity of operators in L[subscript gamma] on homogeneous Sobolev spaces | p. 119 |
| Continuity on ordinary Sobolev spaces | p. 122 |
| Additional remarks | p. 124 |
| The T(b) theorem | |
| Introduction | p. 126 |
| Statement of the fundamental geometric theorem | p. 127 |
| Operators and accretive forms (in the abstract situation) | p. 128 |
| Construction of bases adapted to a bilinear form | p. 130 |
| Tchamitchian's construction | p. 132 |
| Continuity of T | p. 136 |
| A special case of the T(b) theorem | p. 138 |
| An application to the L[superscript 2] continuity of the Cauchy kernel | p. 141 |
| The general case of the T(b) theorem | p. 142 |
| The space H[superscript 1 subscript b] | p. 145 |
| The general statement of the T(b) theorem | p. 149 |
| An application to complex analysis | p. 150 |
| Algebras of operators associated with the T(b) theorem | p. 150 |
| Extensions to the case of vector-valued functions | p. 152 |
| Replacing the complex filed by a Clifford algebra | p. 153 |
| Further remarks | p. 155 |
| Generalized Hardy spaces | |
| Introduction | p. 157 |
| The Lipschitz case | p. 158 |
| Hardy spaces and conformal representations | p. 163 |
| The operators associated with complex analysis | p. 171 |
| The "shortest" proof | p. 178 |
| Statement of David's theorem | p. 181 |
| Transference | p. 185 |
| Calderon-Zygmund decomposition of Ahlfors regular curves | p. 189 |
| The proof of David's theorem | p. 191 |
| Further results | p. 194 |
| Multilinear operators | |
| Introduction | p. 195 |
| The general theory of multilinear operators | p. 197 |
| A criterion for the continuity of multilinear operators | p. 202 |
| Multilinear operators defined on (BMO)[superscript k] | p. 207 |
| The general theory of holomorphic functionals | p. 210 |
| Application to Calderon's programme | p. 215 |
| McIntosh's theory of multilinear operators | p. 220 |
| Conclusion | p. 226 |
| Multilinear analysis of square roots of accretive operators | |
| Introduction | p. 227 |
| Square roots of operators | p. 228 |
| Accretive square roots | p. 232 |
| Accretive sesquilinear forms | p. 236 |
| Kato's conjecture | p. 238 |
| The multilinear operators of Kato's conjecture | p. 239 |
| Estimates of the kernels of the operators L[superscript (2) subscript m] | p. 245 |
| The kernels of the operators L[subscript m] | p. 251 |
| Additional remarks | p. 254 |
| Potential theory in Lipschitz domains | |
| Introduction | p. 255 |
| Statement of the results | p. 256 |
| Almost everywhere existence of the double-layer potential | p. 261 |
| The single-layer potential and its gradient | p. 266 |
| The Jerison and Kenig identities | p. 270 |
| The rest of the proof of Theorems 2 and 3 | p. 274 |
| Appendix | p. 275 |
| Paradifferential operators | |
| Introduction | p. 277 |
| A first example of linearization of a non-linear problem | p. 278 |
| A second linearization of the non-linear problem | p. 280 |
| Paradifferential operators | p. 285 |
| The symbolic calculus for paradifferential operators | p. 288 |
| Application to non-linear partial differential equations | p. 292 |
| Paraproducts and wavelets | p. 294 |
| References and Bibliography | p. 298 |
| References and Bibliography for the English edition | p. 311 |
| Index | p. 313 |
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