JOURNAL BROWSE
Search
Advanced SearchSearch Tips
NOTE ON COMMUTING TOEPLITZ OPERATORS ON THE PLURIHARMONIC BERGMAN SPACE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
NOTE ON COMMUTING TOEPLITZ OPERATORS ON THE PLURIHARMONIC BERGMAN SPACE
Choe, Boo-Rim; Nam, Kye-Sook;
  PDF(new window)
 Abstract
We obtain a characterization of commuting Toeplitz operators with holomorphic symbols acting on the pluriharmonic Bergman space of the polydisk. We also obtain a characterization of normal Toeplitz operators with pluriharmonic symbols. In addition, some results for special types of semi-commutators are included.
 Keywords
Toeplitz operator;pluriharmonic Bergman space;poly disk;
 Language
English
 Cited by
1.
Commuting dual Toeplitz operators on the harmonic Bergman space, Science China Mathematics, 2015, 58, 7, 1461  crossref(new windwow)
2.
The Numerical Range of Toeplitz Operator on the Polydisk, Abstract and Applied Analysis, 2009, 2009, 1  crossref(new windwow)
3.
Commuting dual Toeplitz operators on the harmonic Dirichlet space, Acta Mathematica Sinica, English Series, 2016, 32, 9, 1099  crossref(new windwow)
4.
Commuting Toeplitz operators on the hardy space of the polydisk, Acta Mathematica Sinica, English Series, 2015, 31, 4, 695  crossref(new windwow)
5.
Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball, Journal of Function Spaces, 2016, 2016, 1  crossref(new windwow)
6.
Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space, Journal of Function Spaces and Applications, 2013, 2013, 1  crossref(new windwow)
 References
1.
S. Axler and Z. Cuckovid, Commuting Toeplitz operators with harmonic symbols, Integral Equations Operator Theory, 14 (1991), no. 1, 1-12 crossref(new window)

2.
B. R. Choe, H. Koo, and Y. J. Lee, Commuting Toeplitz operators on the polydisk, Trans. Amer. Math. Soc. 356 (2004), no. 5, 1727-1749 crossref(new window)

3.
B. R. Choe and Y. J. Lee, Commuting Toeplitz operators on the harmonic Bergman space, Michigan Math. J. 46 (1999), no. 1, 163-174 crossref(new window)

4.
Z. Cuckovic, Commuting Toeplitz operators on the Bergman space of an annulus, Michigan Math. J. 43 (1996), no. 2, 355-365 crossref(new window)

5.
S. G. Krantz, Function theory of several complex variables, John Wiley and Sons, New York, 1982

6.
Y. J. Lee and K. Zhu, Some differential and integral equations with applications to Toeplitz operators, Integral Equations Operator Theory 44 (2002), 466-479 crossref(new window)

7.
W. Rudin, Function theory in the unit ball of en, Springer-Verlag, Berlin, Heidelberg, New York, 1980

8.
S. Sun and D. Zheng, Toeplitz operators on the polydisk, Proc. Amer. Math. Soc. 124 (1996), no. 11, 3351-3356

9.
D. Zheng, Commuting Toeplitz operators with pluriharmonic symbols, Trans. Amer. Math. Soc. 350 (1998), no. 4, 1595-1618 crossref(new window)

10.
K. Zhu, Operator theory in function spaces, Marcel Dekker, New York, 1990