Abstract
Linear isometries of N p(D) onto N p(D) are described, where N p(D), p > 1, is the set of all holomorphic functions f on the upper half plane D = {z ∈ ℂ: Im z > 0} such that sup y >0 ∫ℝ lnp (1 + |(x + iy)|) dx < +∞. Our result is an improvement of the results by D.A. Efimov.
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References
Efimov D.A., F-algebras of holomorphic functions in a half-plane defined by maximal functions, Dokl. Math., 2007, 76(2), 755–757
Eoff C.M., A representation of N +α as a union of weighted Hardy spaces, Complex Variables Theory Appl., 1993, 23(3–4), 189–199
Forelli F., The isometries of H p, Canad. J. Math., 1964, 16, 721–728
Iida Y., On an F-algebra of holomorphic functions on the upper half plane, Hokkaido Math. J., 2006, 35(3), 487–495
Iida Y., Mochizuki N., Isometries of some F-algebras of holomorphic functions, Arch. Math. (Basel), 1998, 71(4), 297–300
Mochizuki N., Nevanlinna and Smirnov classes on the upper half plane, Hokkaido Math. J., 1991, 20(3), 609–620
Stein E.M., Weiss G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton Math. Ser., 32, Princeton University Press, Princeton, 1971
Stephenson K., Isometries of the Nevanlinna class, Indiana Univ. Math. J., 1977, 26(2), 307–324
Stoll M., Mean growth and Taylor coefficients of some topological algebras of analytic functions, Ann. Polon. Math., 1977/78, 35(2), 139–158
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Iida, Y., Takahashi, K. Isometries of some F-algebras of holomorphic functions on the upper half plane. centr.eur.j.math. 11, 1034–1038 (2013). https://doi.org/10.2478/s11533-013-0221-0
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DOI: https://doi.org/10.2478/s11533-013-0221-0