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Pure Mathematics 2025
树上加权空间上的加权复合算子
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Abstract:
本文给出了加权
空间之间加权复合算子
的有界性与紧性特征的刻画。
Characterizations of boundedness and compactness of weighted composition operators
between the weighted
spaces are provided.
[1] | Cowen, C.C. and Mac Cluer, B.D. (1999) Composition Operators on Spaces of Analytic Functions. CRC Press. |
[2] | Singh, R.K. and Manhas, J.S. (1993) Composition Operators on Function Spaces. Elsevier. |
[3] | Zhao, R. (2004) Weighted Composition Operators on Bergman Space. Journal of the London Mathematical Society, 70, 499-511. |
[4] | Contreras, M.D. and Hernández-Díaz, A.G. (2003) Weighted Composition Operators between Different Hardy Spaces. Integral Equations and Operator Theory, 46, 165-188. https://doi.org/10.1007/s000200300023 |
[5] | Tien, P.T. and Khoi, L.H. (2018) Weighted Composition Operators between Different Fock Spaces. Potential Analysis, 50, 171-195. https://doi.org/10.1007/s11118-017-9678-y |
[6] | Allen R F, Colonna F, Easley G R. (2011) Multiplication Operators between Lipschitz‐Type Spaces on a Tree. International Journal of Mathematics and Mathematical Sciences, 2011, Article 472495. |
[7] | Hosokawa, T. (2020) Weighted Composition Operators Acting from the Lipschitz Space to the Space of Bounded Functions on a Tree. Acta Scientiarum Mathematicarum, 86, 209-224. https://doi.org/10.14232/actasm-019-522-6 |
[8] | Muthukumar, P., Sharma, A.K. and Kumar, V. (2023) Weighted Composition Operators between Weighted Hardy Spaces on Rooted Trees. Mediterranean Journal of Mathematics, 20, Article No. 61. https://doi.org/10.1007/s00009-023-02269-6 |
[9] | Muthukumar, P. and Ponnusamy, S. (2016) Composition Operators on the Discrete Analogue of Generalized Hardy Space on Homogenous Trees. Bulletin of the Malaysian Mathematical Sciences Society, 40, 1801-1815. https://doi.org/10.1007/s40840-016-0419-y |
[10] | Muthukumar, P. and Ponnusamy, S. (2020) Composition Operators on Hardy Spaces of the Homogenous Rooted Trees. Monatshefte für Mathematik, 192, 721-743. https://doi.org/10.1007/s00605-020-01410-x |
[11] | Muthukumar, P. and Shankar, P. (2022) Multiplication Operators between Discrete Hardy Spaces on Rooted Trees. Lobachevskii Journal of Mathematics, 43, 3252-3263. https://doi.org/10.1134/s1995080222140281 |
[12] | Muthukumar, P. and Ponnusamy, S. (2016) Discrete Analogue of Generalized Hardy Spaces and Multiplication Operators on Homogenous Trees. Analysis and Mathematical Physics, 7, 267-283. https://doi.org/10.1007/s13324-016-0141-9 |
[13] | Allen, R.F. and Sundberg, I. (2015) Multiplication Operators on Weighted Banach Spaces of a Tree. https://doi.org/10.48550/arXiv.1511.07914 |
[14] | Allen, R.F. and Pons, M.A. (2018) Composition Operators on Weighted Banach Spaces of a Tree. Bulletin of the Malaysian Mathematical Sciences Society, 41, 1805-1818. |
[15] | Xu, H. and Zhang, X. (2023) Composition Operators on Weighted Spaces of a Tree. https://doi.org/10.48550/arXiv.2303.10864 |
[16] | Jabłoński, Z., Jung, I.B. and Stochel, J. (2012) Weighted Shifts on Directed Trees. American Mathematical Society. |