Abstract
A theorem is established, asserting that the norm of the derivativef (n)(z) in the space H2 for a functionf(z) regular in the disc is not increased if we replacef by the ratiof (z)/G(z), where G(z) is any interior function dividingf(z) whose singular part is of a particular form.
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L. Carleson, “A representation formula for the Dirichlet integral,” Math. Zeits.,73, No. 2, 190–196 (1960).
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Translated from Matematicheskie Zametki, Vol. 7, No. 2, pp. 165–172, February, 1970.
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Korenblyum, B.I., Korolevich, V.C. Analytic functions which are regular in a disc and smooth on its boundary. Mathematical Notes of the Academy of Sciences of the USSR 7, 100–104 (1970). https://doi.org/10.1007/BF01093490
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DOI: https://doi.org/10.1007/BF01093490