Isometries of some F-algebras of holomorphic functions on the upper half plane

Yasuo Iida; Kei Takahashi

Open Mathematics (2013)

  • Volume: 11, Issue: 6, page 1034-1038
  • ISSN: 2391-5455

Abstract

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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 supy>0 ∫ℝ lnp (1 + |(x + iy)|) dx < +∞. Our result is an improvement of the results by D.A. Efimov.

How to cite

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Yasuo Iida, and Kei Takahashi. "Isometries of some F-algebras of holomorphic functions on the upper half plane." Open Mathematics 11.6 (2013): 1034-1038. <http://eudml.org/doc/268978>.

@article{YasuoIida2013,
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 supy>0 ∫ℝ lnp (1 + |(x + iy)|) dx < +∞. Our result is an improvement of the results by D.A. Efimov.},
author = {Yasuo Iida, Kei Takahashi},
journal = {Open Mathematics},
keywords = {Np(D); Nevanlinna class; Smirnov class; Linear isometry; linear isometry},
language = {eng},
number = {6},
pages = {1034-1038},
title = {Isometries of some F-algebras of holomorphic functions on the upper half plane},
url = {http://eudml.org/doc/268978},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Yasuo Iida
AU - Kei Takahashi
TI - Isometries of some F-algebras of holomorphic functions on the upper half plane
JO - Open Mathematics
PY - 2013
VL - 11
IS - 6
SP - 1034
EP - 1038
AB - 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 supy>0 ∫ℝ lnp (1 + |(x + iy)|) dx < +∞. Our result is an improvement of the results by D.A. Efimov.
LA - eng
KW - Np(D); Nevanlinna class; Smirnov class; Linear isometry; linear isometry
UR - http://eudml.org/doc/268978
ER -

References

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  1. [1] Efimov D.A., F-algebras of holomorphic functions in a half-plane defined by maximal functions, Dokl. Math., 2007, 76(2), 755–757 http://dx.doi.org/10.1134/S1064562407050298[Crossref] Zbl1156.30037
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  3. [3] Forelli F., The isometries of H p, Canad. J. Math., 1964, 16, 721–728 http://dx.doi.org/10.4153/CJM-1964-068-3[Crossref] Zbl0132.09403
  4. [4] Iida Y., On an F-algebra of holomorphic functions on the upper half plane, Hokkaido Math. J., 2006, 35(3), 487–495 Zbl1127.30018
  5. [5] Iida Y., Mochizuki N., Isometries of some F-algebras of holomorphic functions, Arch. Math. (Basel), 1998, 71(4), 297–300 http://dx.doi.org/10.1007/s000130050267[Crossref] Zbl0912.30030
  6. [6] Mochizuki N., Nevanlinna and Smirnov classes on the upper half plane, Hokkaido Math. J., 1991, 20(3), 609–620 Zbl0760.30016
  7. [7] Stein E.M., Weiss G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton Math. Ser., 32, Princeton University Press, Princeton, 1971 Zbl0232.42007
  8. [8] Stephenson K., Isometries of the Nevanlinna class, Indiana Univ. Math. J., 1977, 26(2), 307–324 http://dx.doi.org/10.1512/iumj.1977.26.26023[Crossref] Zbl0326.30025
  9. [9] Stoll M., Mean growth and Taylor coefficients of some topological algebras of analytic functions, Ann. Polon. Math., 1977/78, 35(2), 139–158 Zbl0377.30036

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