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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0221-0,
author = {Yasuo Iida and Kei Takahashi},
title = {Isometries of some F-algebras of holomorphic functions on the upper half plane},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1034-1038},
zbl = {1269.30059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0221-0}
}
Yasuo Iida; Kei Takahashi. Isometries of some F-algebras of holomorphic functions on the upper half plane. Open Mathematics, Tome 11 (2013) pp. 1034-1038. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0221-0/
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