## A real variable method for the Cauchy transform and applications to analytic capacityNagoya University, Dept. of Mathematics, College of General Education, 1987 - Analytic functions - 133 pages |

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### Contents

The Calder6n commutator | 1 |

A real variable method for the Cauchy transform on graphs | 31 |

Analytic capacities of cranks | 71 |

2 other sections not shown

### Common terms and phrases

6-standard kernel absolute constant ac(p analytic capacity analytic functions anti-symmetric assume Banach space Calderon Carleson measure Cauchy transform chord-arc curve cog(K compact set completes the proof component Const a(n Const G Const n Const(l Cotlar's lemma Covering Lemma crank of degree crank of type ct(I curve with constant ds dt ds S Const dx dy dyadic interval estimate exists a crank finite g Const Galton-Watson process give the proof graph Green's formula Hence Hilbert transform inequality holds infimum Lebesgue measure lemmas necessary length Let f log(n+l manner Mf(x midpoint mutually disjoint n-tuple non-negative function norm obtain open set operator defined positive integer pr(E proof of Lemma proof of Theorem Q.E.D. Lemma required inequality RSL of Type sequence shows singular integral operator supremum is taken TQ(n