重调和Hardy空间Toeplitz算子的交换性
Commuting Toeplitz Operators on the Pluriharmonic Hardy Space
本文研究重调和Hardy空间h2(∂Ω)上Toeplitz算子的交换性,给出了h2(T2)上一个解析Toeplitz算子与另一个共轭解析Toeplitz算子交换的充分必要条件.
We study the commuting Toeplitz operators on the pluriharmonic Hardy space h2(∂Ω). A necessary and sufficient condition is obtained for an analytic Toeplitz operator and a co-analytic Toeplitz operator to be commuting on h2(T2).
多重调和Hardy空间 / Toeplitz算子 / Berezin变换 {{custom_keyword}} /
pluriharmonic Hardy space / Toeplitz operator / Berezin transform {{custom_keyword}} /
[1] Axler S., Bergman Space and Their Operators, Surveys of Some Recent Results in Operator Theory, Vol.1, Pitman Research Notes Math. Ser., 1988, 171:1-50.
[2] Brown B., Halmos P. R., Algebraic properties of Toeplitz operators, J. Reine Angew. Math., 1964, 213:1063-1064; 89-102.
[3] Choe B. R., Lee Y. J., Commuting Toeplitz operators on the harmonic Bergman space, Michigan Math. J., 1999, 46:163-174.
[4] Davie A. M., Jewell N. P., Toeplitz operators in several complex variables, J. Funct Anal., 1977, 26:356-368.
[5] Ding X., The commutator of Toeplitz operators on torus, Acta Math. Sin. Chin. Ser., 2002, 4:655-660.
[6] Ding X., Compact Product of Toeplitz operators on the polydisk, Acta Math. Sin. Chin. Ser., 2005, 3:493-498.
[7] Ding X., Products of Toeplitz operators on the polydisk, Integr. Equ. Oper. Theory, 2003, 45:389-403.
[8] Douglas R. G., Banach Algebra Techniques in Operator Theory, Vol. 179, Springer Science & Business Media, 2012.
[9] Engliš M., Toeplitz operators and the Berezin transform on H2, Linear Algebra Appl., 1995, 223:171-204.
[10] Gu C., Some algebraic properties of Toeplitz and Hankel operators on polydisk, Archiv der Mathematik, 2003, 80:393-405.
[11] Gu C., Zheng D., The semi-commutator of Toeplitz operators on the bidisc, J. Operator Theory, 1997, 38:173-193.
[12] Guo K., Zheng D., Toeplitz algebra and Hankel algebra on the harmonic Bergman space, J. Math. Anal. Appl., 2002, 276:213-230.
[13] Liu Y., Ding X., Toeplitz operators on the pluriharmonic Hardy space (in Chinese), Sci. Sin. Math., 2013, 43(7):675-690.
[14] Rudin W., Function Theory in Polydiscs, Vol. 41, WA Benjamin, 1969.
[15] Rudin W., Function Theory on the Unit Ball of Cn, Grundlehren, Vol. 241, Springer-Verlag, Berlin, 1980.
国家自然科学基金资助项目(11271388)
/
〈 | 〉 |