β-Hausdorff Operator on Lipschitz Space in the Unit Polydisk
Affiliation(s)
School of Mathematics and Finance-Economics, Sichuan University of Arts and Science, Dazhou, China.
School of Mathematics and Finance-Economics, Sichuan University of Arts and Science, Dazhou, China.
ABSTRACT
In this paper, we define β-Hausdorff operator on the unit polydisk and study the boundedness of the operator on Lipschitz space. Firstly, we translate the problem of coefficient into integral of weighted composition operator, then give the sufficient conditions of boundedness, and also obtain an upper bound for the operator norm on Lipschitz space.
Cite this paper
Zhang, C. and Hu, R. (2014) β-Hausdorff Operator on Lipschitz Space in the Unit Polydisk. Advances in Pure Mathematics, 4, 171-175. doi: 10.4236/apm.2014.45022.
Zhang, C. and Hu, R. (2014) β-Hausdorff Operator on Lipschitz Space in the Unit Polydisk. Advances in Pure Mathematics, 4, 171-175. doi: 10.4236/apm.2014.45022.
References
[1] Garabedian, H.L. (1939) Hausdorff Matrices. The American Mathematical Monthly, 46, 390-410.
http://dx.doi.org/10.2307/2303033 [2] Zhou, Z.H. (2003) Composition Operators on the Lipschitz Space in Polydiscs. Science in China, 46, 33-38.
http://dx.doi.org/10.1360/03ys9004 [3] Chang, D.C., Gilbert, R. and Stevi, S. (2006) Hausdorff Operator on the Unit Polydisk in . Complex Variables and Elliptic Equations, 4, 329-345.
http://dx.doi.org/10.1080/17476930600610528 [4] Hu R., Xie L. and Hu, P.Y. (2012) Hausdorff-Type Operator on Bloch Space in the Unit Polydisk in . Acta Mathematica Scientia, 32, 521-529. [5] Timoney, R.M. (1980) Blochfunctions in Several Complex Variables. Bull London Math, 319, 1-22. [6] Zhou, Z.H. and Wei, Z.Q. (2005) Weighted Composition Operators on the Bloch Space in Polydiscs. Journal of Mathematics, 25, 435-440 [7] Galanopoulos, P. and Siskakis, A. (2001) Hausdorff Matrices and Composition Operators. Illinois Hournal of Math, 45, 757-773. [8] Liflyand, E. and Móricz, F. (2000) The Hausdorff Operator Is Bounded on the Real Hardy Space. Proceedings of the American Mathematical Society, 128, 1391-1396.
http://dx.doi.org/10.1090/S0002-9939-99-05159-X [9] Zhou Z.H. and Shi J.H. (2001) Composition Operators on the Bloch Space in Polydiscs. Complex Variables, 46, 73-88.
http://dx.doi.org/10.1080/17476930108815398
[1] Garabedian, H.L. (1939) Hausdorff Matrices. The American Mathematical Monthly, 46, 390-410.
http://dx.doi.org/10.2307/2303033 [2] Zhou, Z.H. (2003) Composition Operators on the Lipschitz Space in Polydiscs. Science in China, 46, 33-38.
http://dx.doi.org/10.1360/03ys9004 [3] Chang, D.C., Gilbert, R. and Stevi, S. (2006) Hausdorff Operator on the Unit Polydisk in . Complex Variables and Elliptic Equations, 4, 329-345.
http://dx.doi.org/10.1080/17476930600610528 [4] Hu R., Xie L. and Hu, P.Y. (2012) Hausdorff-Type Operator on Bloch Space in the Unit Polydisk in . Acta Mathematica Scientia, 32, 521-529. [5] Timoney, R.M. (1980) Blochfunctions in Several Complex Variables. Bull London Math, 319, 1-22. [6] Zhou, Z.H. and Wei, Z.Q. (2005) Weighted Composition Operators on the Bloch Space in Polydiscs. Journal of Mathematics, 25, 435-440 [7] Galanopoulos, P. and Siskakis, A. (2001) Hausdorff Matrices and Composition Operators. Illinois Hournal of Math, 45, 757-773. [8] Liflyand, E. and Móricz, F. (2000) The Hausdorff Operator Is Bounded on the Real Hardy Space. Proceedings of the American Mathematical Society, 128, 1391-1396.
http://dx.doi.org/10.1090/S0002-9939-99-05159-X [9] Zhou Z.H. and Shi J.H. (2001) Composition Operators on the Bloch Space in Polydiscs. Complex Variables, 46, 73-88.
http://dx.doi.org/10.1080/17476930108815398