Index Ax weights, 38, 134, 140 Ap weights, 133, 135 and BMO, 151 factorization of, 136, 150 reverse Holder inequality, 137, 151 two weight condition, 154 Aoo weights, 139, 149, 152 and doubling measures, 149 Abel-Poisson summability, 10, 18, 25, 32 Ahlfors-David curves, 213 Ap (strong Ap weights), 152 and strong maximal function, 153 factorization of, 153 approximation of the identity, 25, 31 atoms, 115 Banach-Steinhaus theorem, 6 Besicovitch-Morse covering lemma, 44 Besov spaces, 185 Bessel functions, 171 bilinear Hilbert transform, 214 BMO (bounded mean oscillation), 117 and Ap weights, 151 and Carleson measures, 199 and commutators, 131 and interpolation, 121 dual of if1, 129 logarithmic growth, 123, 125 Bochner's theorem, 23 Bochner-Hecke formula, 85 Bochner-Riesz multipliers, 47, 169, 187 and restriction theorems, 189 critical index of, 169 Co, 14, 131 C£°, xviii C~ 0 , 201 C£, 215 Calderon commutators, 100, 203, 213 conjecture, 214 Calderon-Zygmund decomposition, 34 weighted, 150 operators, 98, 100 maximal, 102 norm inequalities, 99 singular integrals, 102 theorem, 91 Carleson measures, 197 and BMO, 199 and Poisson integrals, 198 Carleson-Hunt theorem, 9, 18 Cauchy integral, 99, 109, 205, 213 Cesaro summability, 9, 18, 25, 32, 168 and Gibbs phenomenon, 21 Chebyshev inequality, 27 Coifman-Fefferman inequality, 152 commutators, 131 conjugate function, 61, 155 conjugate Poisson kernel, 50, 62 convolution, xviii Fourier transform of, 11 Cotlar's inequality, 56, 102, 147 lemma, 114, 195 covering lemmas, 31, 44 Besicovitch-Morse, 44 Vitali-type, 44 219
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