## Banach Spaces of Analytic Functions: AMS Special Session, April 22-23, 2006, University of New Hampshire, Durham, New HampshireThis volume is focused on Banach spaces of functions analytic in the open unit disc, such as the classical Hardy and Bergman spaces, and weighted versions of these spaces. Other spaces under consideration here include the Bloch space, the families of Cauchy transforms and fractional Cauchy transforms, BMO, VMO, and the Fock space. Some of the work deals with questions about functions in several complex variables. Multiplication operators, composition operators and weighted composition operators form a central topic of the volume. This topic has been an extensive area of research for the past twenty years. This volume includes results characterizing bounded, compact and isometric composition operators in various settings. Graduate students who are interested in analysis will find an overview of current work in the field. Specialists will find interesting questions and new methods, as well as familiar ideas (such as composition operators) seen in new settings or in more general form. Mathematicians with an interest in modern analysis will gain insight into the interplay between function theory and operator theory which is central to this work. |

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### Contents

1 | |

On the inverse of an analytic mapping | 5 |

Isometric composition operators on the Bloch space in the polydisc | 9 |

Pluripolarity of manifolds | 23 |

On a question of Brézis and Korevaar concerning a class of squaresummable sequences | 35 |

Approximating z in Hardy and Bergman Norms | 43 |

A general view of multipliers and composition operators II | 63 |

A general view of BMO and VMO | 75 |

Order bounded weighted composition operators | 93 |

Fractional Cauchy transforms and composition | 107 |

Continuous functions in starinvariant subspaces The Abstract | 117 |

Indestructible Blaschke products | 119 |

On Taylor coefficients and multipliers in Fock spaces | 135 |

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&max Alec algebra Amer American Mathematical Society analytic functions annulus Ap(G approacimation Aut(A automorphisms Banach space Bergman metric Bergman spaces best approximation Blaschke product Bloch functions Bloch semi-norm Bloch space BMO(T,p Borel boundary component Cauchy transforms characterization compact subset composition operators Contemporary Mathematics Volume continuous function convergence Corollary cospace define denote domain Ep(G exists finite Fock space follows Frostman function f Gevrey class Hardy spaces Hence holomorphic functions implies indestructible inequality isometric composition operators isometry K-dim Khavinson Kolmogorov lacunary sequence Lebesgue Lemma linear Math Mathematics Subject Classification Mathematics Volume 454 Matheson measure multiplier pair order bounded pluripolar polydisk polynomials proof of Theorem Proposition prove result satisfies Smirnov ſº Suppose Theorem 3.2 unit ball unit disk yields