SOME RESULTS ON GENERALIZED TOEPLITZ OPERATOR ON GENERALIZED HARDY SPACE

Yıl 2016, Cilt: 6 Sayı: 2, 185 - 192, 01.12.2016

Sh. Al-sharif Y. Jebreel A. Khanfer

Öz

In this paper, we dene and study some properties of the generalized Hardy space HF;2; where F is an injective linear transform from Lp  into Lp  and  is the unit circle in the complex plane C: Also we introduce the concept of a generalized Toeplitz operator on HF;2 and prove some of its properties. Further results are presented.

Anahtar Kelimeler

Hardy space, Toeplitz operator.

Kaynakça

• Abrahamse,M.B., (1971), Toeplitz operators in multiply connected regions, Bull. Amer. Math. Soc., Vol. 771971, pp. 449-454.
• Diestel,J. and Uhl,J.R., (1977), Vector Measures, Amer. Math. Soc. Math. Surveys, Vol. 15.
• Douglas,R.G., (1972), Banach Algebra Techniques in Operator Theory. Academic Press.
• Faour,N.S., (1982), Toeplitz operators on Bergmann and Hardy spaces, Houston J. Math., Vol. 18, pp. 185-191.
• Fatehi,M., (2010), On the generalized Hardy spaces, Abs. and appl. anal., Vol. 2010, pp. 1-14.
• Rabindranathan,M., (1969), On the inversion of Toeplitz operators, J. Math. Mech., Vol. 19.
• Rochberg,R., (1977), Toeplitz operators on weighted Hpspaces, Indiana Univ. Math. J., Vol. 26, pp. 291-298.
• Vukoti´c,D., (2003), Analytic Toeplitz operators on the Hardy space Hp: A Survey, Bull. Belg. Math. Soc., Vol.10, pp. 101-113.
• Wermer,J., (1976), Banach Algebras and Several Complex Variables, Springer-Verlag.
• Widom,H., (1966), Toeplitz operators on Hp, Pacific J. Math., Vol. 19, pp. 573-582.
• Sharifa Al-Sharif, for the photograph and short biography, see TWMS J. Appl. and Eng. Math., V.4, No.2, 2014.