The Effects of Weight-Doubling Sequences on the Compactness of Differences of Composition Operators on Bergman Spaces
DOI:
https://doi.org/10.17605/OSF.IO/CF36GKeywords:
Bergman space, Carleson measure, doubling weight, composition operator.Abstract
Differences that are bounded and compact between two composition operators that are acting from the weighted Bergman space to the Lebesgue space , where and class of radial weights with a two-sided doubling requirement. New description of -Carleson measures for , with and , Using discs of pseudohyperbolic geometry is proven. This last theorem generalizes the standard definition of - Carleson uses weights as a baseline for the Bergman space he creates. with to the setting of doubling weights. The case is also briefly talked about, and a question is raised about this case.
References
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Peláez, José Ángel; Rättyä, Jouni; Sierra, Kian: Atomic decomposition and Carleson measures for weighted Mixed norm spaces. J. Geom. Anal. (2019), 1-33.
Saadeh, R., A. Abdoon, M., Qazza, A., & Berir, M. (2023). A Numerical Solution of Generalized Caputo Fractional Initial Value Problems. Fractal and Fractional, 7(4), 332.
Qazza, A., Abdoon, M., Saadeh, R., & Berir, M. (2023). A New Scheme for Solving a Fractional Differential Equation and a Chaotic System. European Journal of Pure and Applied Mathematics, 16(2), 1128-1139.
Abdoon, M. A., Saadeh, R., Berir, M., & Guma, F. E. (2023). Analysis, modeling and simulation of a fractional-order influenza model. Alexandria Engineering Journal, 74, 231-240.
Cowen, Carl C.; MacCluer, Barbara D.: Composition operators on spaces of analytic functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1995. xii +388pp.
Shapiro, Joel H.: The essential norm of a composition operator. Ann. of Math. (2) 125 (1987), 375-404.
Shapiro, Joel H.: Composition operators and classical function theory. Universitext: Tracts in Mathematics. Springer-Verlag, New York, 1993.
Zhu, K.: Operator Theory in Function Spaces. American Mathematical Society, Providence, RI. 2007.
Shapiro, Joel H.; Sundberg, Carl: Isolation amongst the composition operators. Pacific J. Math. 145(1990),117-152.
Luecking, Daniel H., Embedding theorems for spaces of analytic functions via Khinchine's inequality, Michigan Math. J. 40 (1993), 333-358.
Choe, Boo Rim; Koo, Hyungwoon; Park, Inyoung: Compact differences of composition operators on the Bergman spaces over the ball. Potential Anal. 40(2014), 〖81〗^∘ C102.
Goebeler, Thomas E., Jr.: Composition operators acting between Hardy spaces. Integral Equations Operator Theory 41 (2001), 389-395.
Liu, Bin; Rättyä, Jouni, Compact differences of weighted composition operators, preprint. https://arxiv.org/pdf/2005.12016.pdf
Nieminen, Pekka J.; Saksman, Eero: On compactness of the difference of composition operators. J. Math. Anal. Appl. 298(2004),501-522.
Choe, Boo Rim; Choi, Koeun; Koo, Hyungwoon; Yang, Jongho: Difference of weighted composition operators. J. Funct. Anal. 278(2020),108401,38pp.
Moorhouse, Jennifer: Compact differences of composition operators. J. Funct. Anal. 219 (2005), 70-92.
Saukko, Erno: Difference of composition operators between standard weighted Bergman spaces. J. Math. Anal. Appl. 381 (2011), 789-798.
Saukko, Erno: An application of atomic decomposition in Bergman spaces to the study of differences of composition operators. J. Funct. Anal. 262(2012),3872-3890.
Shi,Y.; Li,S.; Du,J.: Difference of composition operators between weighted Bergman spaces on the unit ball. https://arxiv.org/pdf/1903.00651.pdf.
Duren, Peter; Schuster, Alexander Bergman spaces. Mathematical Surveys and Monographs, 100. American Mathematical Society, Providence, RI, 2004. (35) Volume (3) December 2022; [UBJSR: ISSN [1858-6139]: (Online)
Hedenmalm, Haakan; Korenblum, Boris; Zhu, Kehe Theory of Bergman spaces. Graduate Texts in Mathematics, 199. Springer-Verlag, New York, 2000.
Peláez, José Ángel and Rättyä, Jouni: Bergman projection induced by radial weight, https:// arxiv.org/pdf/1902.09837.pdf.
Peláez, José Ángel and Rättyä, Jouni: Embedding theorems for Bergman spaces via harmonic analysis, Math. Ann. 362 (2015), 205-239.
Peláez, José Ángel: Small weighted Bergman spaces, Proceedings of the summer school in complex and harmonic analysis, and related topics, (2016).
Peláez, José Ángel; Rättyä, Jouni: Weighted Bergman spaces induced by rapidly increasing weights. Mem. Amer. Math. Soc. 227 (2014), no. 1066, vi+124pp.
Peláez, José Ángel; Rättyä, Jouni; Sierra, Kian: Embedding Bergman spaces into tent spaces, Math.Z, 281(2015),1215 - 1237.
Shi, Yecheng; Li, Songxiao Difference of composition operators between different Hardy spaces. J. Math. Anal. Appl. 467(2018),1-14.
Halmos, Paul R. : Measure Theory, Springer-Verlag, New York, 1974.
Bin Liu, Jouni Rättyä, and Fanglei Wu, Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights, The J. of Geometric Analysis, 31, 2021, 12485-12500.
Peláez, José Ángel; Rättyä, Jouni; Sierra, Kian: Atomic decomposition and Carleson measures for weighted Mixed norm spaces. J. Geom. Anal. (2019), 1-33.
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Published
2023-05-15
How to Cite
Salih Yousuf Mohamed Salih, & Shahinaz.A. Elsamani. (2023). The Effects of Weight-Doubling Sequences on the Compactness of Differences of Composition Operators on Bergman Spaces. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 4(5), 120–133. https://doi.org/10.17605/OSF.IO/CF36G
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