Hp uzaylarının dualliklerinin uygulamaları

We present several classical theorems on Hardy spaces that have in common theidea of duality. Thus, we prove the Rogosinski-Shapiro theorems on realizations ofthe distance to Hp , the Sarason Theorem on the algebra C + H∞ , V.M. Adamyan,D.Z. Arov, and M.G. Krein Theorem stating that if F ∈ L∞ and F − H∞ ∞ < 1then F + H∞ contains an element ω whose modulus is 1 almost everywhere,D. Marshall Theorem stating that the closed unit ball of H∞ is the closed convexhull of the set of all Blaschke products, as well as G. Szegü Theorem providing aoformula to calculate the distance in Lp (µ), where µ is a positive Borel measure on[−π, π], of the function 1 to the algebra of polynomials vanishing at 0, in termsof the Radon-Nykodim derivative of µ with respect to the Lebesgue measure.Keywords: Hardy spaces.i