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THE SPACE H1 56
FACTORIZATION FOR Hp FUNCTIONS 79
ANALYTIC FUNCTIONS WITH CONTINUOUS
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absolutely continuous analytic function Baire function Baire set Banach space Blaschke product boundary values bounded analytic function closed disc closed ideal commutative Banach algebra complex numbers constant continuous functions converges Corollary countable defined denote Dirichlet algebra everywhere f is analytic Fourier coefficients Fourier series function f function in H H dm Hilbert space homomorphism imaginary axis inequality infinite product inner function inner product invariant subspaces invariant under multiplication isometry last theorem Lebesgue measure Lemma Let f Let g Let H log h log|f maximal ideal modulus non-negative non-tangential limits obtain open disc operator on H orthogonal to Aq outer function Poisson integral polynomials positive Baire measure positive measure positive singular measure Proof prove quotient real-valued Riesz right half-plane sequence shift operator singular measure space H subspace of H Suppose f topology TT TT uniformly closed unit circle unit disc unitary vanish weak-star