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

• Autorzy: Yasuo Iida , Kei Takahashi
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Np(D); Nevanlinna class; Smirnov class; Linear isometry

Kategorie tematyczne

• 30H50: Algebras of analytic functions
• 46E10: Topological linear spaces of continuous, differentiable or analytic functions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 6
• Strony: 1034-1038

Daty

wydano

2013-06-01

online

2013-03-28

Twórcy

autor

Yasuo Iida

• Department of Mathematics, Iwate Medical University, Yahaba, Iwate, 028-3694, Japan

autor

Kei Takahashi

• Department of Mathematics, Iwate Medical University, Yahaba, Iwate, 028-3694, Japan

Bibliografia

• [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]
• [2] 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 http://dx.doi.org/10.1080/17476939308814684[Crossref]
• [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]
• [4] Iida Y., On an F-algebra of holomorphic functions on the upper half plane, Hokkaido Math. J., 2006, 35(3), 487–495
• [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]
• [6] Mochizuki N., Nevanlinna and Smirnov classes on the upper half plane, Hokkaido Math. J., 1991, 20(3), 609–620
• [7] Stein E.M., Weiss G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton Math. Ser., 32, Princeton University Press, Princeton, 1971
• [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]
• [9] Stoll M., Mean growth and Taylor coefficients of some topological algebras of analytic functions, Ann. Polon. Math., 1977/78, 35(2), 139–158

Identyfikatory

DOI

10.2478/s11533-013-0221-0