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Studia Mathematica

1992 | 102 | 1 | 57-75
Tytuł artykułu

Orthogonal polynomials and middle Hankel operators on Bergman spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We introduce a sequence of Hankel style operators $H^k$, k = 1,2,3,..., which act on the Bergman space of the unit disk. These operators are intermediate between the classical big and small Hankel operators. We study the boundedness and Schatten-von Neumann properties of the $H^k$ and show, among other things, that $H^k$ are cut-off at 1/k. Recall that the big Hankel operator is cut-off at 1 and the small Hankel operator at 0.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
57-75
Opis fizyczny
Daty
wydano
1992
otrzymano
1991-09-10
Twórcy
autor
• Department of Mathematics, Peking University, Beijing 100871, P.R. China.
autor
• Department of Mathematics, Washington University, St. Louis, Missouri 63130, U.S.A., rr@jezebel.wustl.edu
autor
• Department of Mathematics, University of Alabama Tuscaloosa, Alabama 35487, U.S.A., zwu@ua1vm.ua.edu
Bibliografia
• [AFP] J. Arazy, S. Fisher and J. Peetre, Hankel operators on weighted Bergman spaces, Amer. J. Math. 110 (1988), 989-1054.
• [A] S. Axler, The Bergman space, the Bloch space, and commutators of multiplication operators, Duke Math. J. 53 (1986), 315-332.
• [J1] S. Janson, Hankel operators between weighted Bergman spaces, Ark. Mat. 26 (1988), 205-219.
• [J2] S. Janson, Hankel operators on Bergman spaces with change of weight, Mittag-Leffler report, 1991.
• [JR] S. Janson and R. Rochberg, Intermediate Hankel operators on the Bergman space, J. Operator Theory, to appear.
• [JP] Q. Jiang and L. Peng, Wavelet transform and Ha-Plitz operators, preprint, 1991.
• [N] K. Nowak, Estimate for singular values of commutators on weighted Bergman spaces, Indiana Univ. Math. J., to appear.
• [M] M. M. Peloso, Besov spaces, mean oscillation, and generalized Hankel operators, preprint, 1991.
• [P] J. Peetre, New Thoughts on Besov Spaces, Duke Univ. Math. Ser. 1, Durham 1976.
• [Pel1] V. V. Peller, Vectorial Hankel operators, commutators and related operators of the Schatten-von Neumann class $S_p$, Integral Equations Operator Theory 5 (1982), 244-272.
• [Pel2] V. V. Peller, A description of Hankel operators of class $S_p$ for p > 0, investigation of the rate of rational approximation, and other applications, Math. USSR-Sb. 50 (1985), 465-494.
• [PX] L. Peng and C. Xu, Jacobi polynomials and Toeplitz-Hankel type operators on weighted Bergman spaces, preprint, 1991.
• [PZ] L. Peng and G. Zhang, Middle Hankel operators on Bergman space, preprint, 1990.
• [R1] R. Rochberg, Trace ideal criteria for Hankel operators and commutators, Indiana Univ. Math. J. 31 (1982), 913-925.
• [R2] R. Rochberg, Decomposition theorems for Bergman spaces and their applications, in: Operators and Function Theory, Reidel, Dordrecht 1985, 225-277.
• [S] S. Semmes, Trace ideal criteria for Hankel operators, and applications to Besov spaces, Integral Equations Operator Theory 7 (1984), 241-281.
• [Sz] G. Szegö, Orthogonal Polynomials, Colloq. Publ. 23, 4th ed., Amer. Math. Soc., Providence, R.I., 1975.
• [Z] G. Zhang, Hankel operators and Plancherel formula, Ph.D thesis, Stockholm University, Stockholm 1991.
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Bibliografia
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