## Generalized Restriction Theorems for Analytic Functions |

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### Contents

SUBSPACES OF GENERAL L2Xdy SPACES WHOSE FUNCTIONS | 43 |

IDENTIFICATION AND RECAPTURE OF H2 0I+xII+ FUNCTIONS | 62 |

GENERALIZATION OF A THEOREM OF KORANYI | 77 |

2 other sections not shown

### Common terms and phrases

2N Re zi Amer Analytic Functions b.fz b.Tb b.Tc best possible constant Borel set boundary restriction bounded mean oscillation bounded nonnegative measure bounded operator bounded solution boundedness bT-Tb Cauchy principal value Chapter characterization closed subspace condition Corollary defined denote example F satisfies f,b.S g function F H n xn H X,dy Hardy space Hence Hilbert space Hilbert transform holds implies inequality integral representation Koranyi Lebesgue measure Lemma linear Loewner's theorem Math measurable function multiplication n-torus N,n N,n N,n nonnegative imaginary norm Note obtain operator equation orthogonal projection pointwise a.e. positive measure Proof restriction theorems Riesz property Rosenblum and Rovnyak rotational invariant subspaces satisfies 58 selfadjoint sequence set of positive space H subset Suppose tends to zero Toeplitz operator trigonometric polynomials vanish variable weak Dirichlet algebra weighted space