Abstract
We completely describe the boundedness and compactness of Hankel operators with general symbols acting on Bergman spaces with exponential type weights.
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Arroussi H. Function and operator theory on large Bergman spaces. PhD Thesis. Barcelona: Universität de Barcelona, 2016
Arroussi H, Park I, Pau J. Schatten class Toeplitz operators acting on large weighted Bergman spaces. Studia Math, 2015, 229: 203–221
Borichev A, Dhuez R, Kellay K. Sampling and interpolation in large Bergman and Fock spaces. J Funct Anal, 2007, 242: 563–606
Chen S, Shaw M. Partial Differential Equations in Several Complex Variables. AMS/IP Studies in Advanced Mathematics, vol. 19. Providence: Amer Math Soc, 2001
Constantin O, Ortega-Cerdà J. Some spectral properties of the canonical solution operator to \(\overline \partial \) on weighted Fock spaces. J Math Anal Appl, 2011, 377: 353–361
Constantin O, Peláez J A. Boundedness of the Bergman projection on Lp spaces with exponential weights. Bull Sci Math, 2015, 139: 245–268
Constantin O, Peláez J A. Integral operators, embedding theorems and a Littlewood-Paley formula on weighted Fock spaces. J Geom Anal, 2016, 26: 1109–1154
El-Fallah O, Mahzouli H, Marrhich I, et al. Asymptotic behavior of eigenvalues of Toeplitz operators on the weighted analytic spaces. J Funct Anal, 2016, 270: 4614–4630
Galanopoulos P, Pau J. Hankel operators on large weighted Bergman spaces. Ann Acad Sci Fenn Math, 2012, 37: 635–648
Hu Z, Lv X, Schuster A P. Bergman spaces with exponential weights. J Funct Anal, 2019, 276: 1402–1429
Hu Z, Wang E. Hankel operators between Fock spaces. Integral Equations Operator Theory, 2018, 90: 37, 20pp
Luecking D H. Characterizations of certain classes of Hankel operators on the Bergman spaces of the unit disk. J Funct Anal, 1992, 110: 247–271
Luecking D H. Embedding theorems for spaces of analytic functions via Khinchine’s inequality. Michigan Math J, 1993, 40: 333–358
Pau J, Peláez J A. Embedding theorems and integration operators on Bergman spaces with rapidly decreasing weights. J Funct Anal, 2010, 259: 2727–2756
Pau J, Peláez J A. Volterra type operators on Bergman spaces with exponential weights. Contemp Math, 2012, 561: 239–252
Zhu K. Operator Theory in Function Spaces, 2nd ed. Mathematical Surveys and Monographs, vol. 138. Providence: Amer Math Soc, 2007
Acknowledgements
The first author was supported by National Natural Science Foundation of China (Grant No. 11771139). The second author was supported by Ministerio de Educación y Ciencia (Grant No. MTM2017-83499-P) and Generalitat de Catalunya (Grant No. 2017SGR358). Part of the work was done while the first author visited the Department of Mathematics at University of Barcelona to which the first author expresses thanks for the hospitality and stimulating environment. The authors thank the referees for their careful reading and helpful suggestions.
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Hu, Z., Pau, J. Hankel operators on exponential Bergman spaces. Sci. China Math. 65, 421–442 (2022). https://doi.org/10.1007/s11425-020-1724-3
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DOI: https://doi.org/10.1007/s11425-020-1724-3