## The BP Spaces of an Annulus |

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### Contents

CONTENTS | 4 |

Definitions and immediate properties of the spaces HA and HdA | 10 |

Harmonic functions in | 21 |

3 other sections not shown

### Common terms and phrases

absolutely continuous analytic functions angular measure annulus automorphlc Banach space belongs to HP(D Blaschke product boundary function boundary measure induced boundary values bounded characteristic bounded linear Cauchy integral formula class L(A codimension conclude constant of unit converges COROLLARY defined denote disk doubly invariant subspace Ds[F Ds[x eigenvalue f belongs F in HP(A factorization of F finite real Borel Fourier series func function in HP(A functions of class Ha(A harmonic function Hence holomorphic function Hp spaces Hp(dA implies index of F induced by F inner function Is[x Jensen's formula Jensen's inequality Kas'yanyuk kernel L(Fjr Lebesgue measure Lemma Let f Lp(dA maps modulus almost everywhere modulus automorphic function multiplicative constant number in 0,1 orthogonal outer function point r,t properties prove real number respect to angular result Rs[x satisfies Section sequence series of x|C singular function spaces HP(A Suppose Theorem 15 tion unique unit modulus vanish zeros or poles