The Effects of Weight-Doubling Sequences on the Compactness of Differences of Composition Operators on Bergman Spaces
Keywords:
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.
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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.
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.
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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