Abstract
This paper is devoted to studying Bergman spaces \(A_{\omega_{1,2}}^{p}(M)(1<p<\infty)\) induced by regular-weight ω1,2 on annulus M. We characterize the function f in \(L_{\omega_{1,2}}^{1}(M)\) for which the induced Hankel operator Hf is bounded (or compact) from \(A_{\omega_{1,2}}^{p}(M)\) to \(L_{\omega_{1,2}}^{1}(M)\) with 1 < p, q < ∞.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Arazy, J., Fisher, S. D., Peetre, J.: Hankel operators on weighted Bergman spaces. American Journal of Mathematics, 110(6), 989–1053 (1988)
Cao, G.: Toeplitz operators on bergman spaces of multiply connected domains. Chinese Annals of Mathematics, 5(5), 671–678 (2008)
Chen, S., Shaw, M.: Partial Differential Equations in Several Complex Variables. AMS/IP Studies in Advanced Mathematics, 19. American Mathematical Society, Providence, RI; International Press, Boston, MA, 2001
Békollé, D., Berger, C. A., Coburn, L. A., Zhu, K. H.: BMO in the Bergman metric on bounded symmetric domains. Journal of Functional Analysis, 93(2), 310–350 (1990)
Hu, Z., Jin, L.: Hankel operators on Bergman spaces with regular weights. J. Geom. Anal., 29(4), 3494–3519 (2019)
Hu, Z., Wang, E.: Hankel operators between Fock spaces. Integr. Equ. Oper. Theory, 90(3), Paper No. 37, 20pp. (2018)
Jovovic, M., Zheng, D.: Compact operators and Toeplitz algebras on multiply-connected domains. Journal of Functional Analysis, 261(1), 25–50 (2011)
Li, H.: Compact Hankel operators on multiply connected domains. Journal of Mathematical Analysis and Applications, 171(2), 588–592 (1992)
Li, H.: Hankel operators on the Bergman space of multiply-connected domains. Journal of Operator Theory, 321–335 (1992)
Luecking, D. H.: Characterizations of certain classes of Hankel operators on the Bergman spaces of the unit disk. J. Funct. Anal., 110, 247–271 (1992)
Luecking, D. H.: Embedding theorems for spaces of analytic functions via Khintchines inequality. Mich. Math. J., 40(2), 333–358 (1993)
Pau, J., Zhao, R., Zhu, K.: Weighted BMO and Hankel operators between Bergman spaces. Indiana Univ Math J., 65, 1639–1673 (2016)
Pavlovic, M., Peláez, J. A.: An equivalence for weighted integrals of an analytic function and its derivative. Mathematische Nachrichten, 281(11), 1612–1623 (2008)
Peláez, J. A.: Small weighted Bergman spaces. In: Proceedings of the Summer School in Complex and Harmonic Analysis, and Related Topics, 29–98, Univ. East. Finl., Fac. Sci. For., Jolnnuu, 2016
Peláez, J. A., Rättyä, J., Sierra, A. K.: Berezin transform and Toeplitz operators on Bergman spaces induced by regular weights. J. Geom. Anal., 28, 656–687 (2018)
Peléez, J. A., Rättyä, J.: Weighted Bergman spaces induced by rapidly increasing weights. Mem. Math. Soc., 227(1066), 1–119 (2014)
Peláez, A., Schuster, A., Virtanen, J. A.: Hankel operators on Fock spaces. In: Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, Vol. 236, 377–390 (2014)
Peller, V.: Hankel Operators and Their Applications, Springer Science, Business Media, 2012
Seip, K., Youssfi, E. H.: Hankel operators on Fock spaces and related Bergman kernel estimates. J. Geom. Anal., 25(1), 170–201 (2013)
Wang, X. F., Cao, G. F., Zhu, K. H.: BMO and Hankel operators on Fock-type spaces. J. Geom. Anal. 25(3), 1650–1665 (2015)
He, Z. H., Wang, X. F., Xia J.: Positive Toeplitz operators on Bergman space of annular induced by regular-weight, Preprint (2019)
Zhu, K.: Operator Theory in Function Spaces: Second Edition. Mathematical Surveys and Monographs, 138. American Mathematical Society, 2007
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by NNSF of China (Grant Nos. 11971125, 11471084)
Rights and permissions
About this article
Cite this article
Yang, L.H., Wang, X.F. & Xia, J. Hankel Operators on Bergman Spaces of Annulus Induced by Regular Weights. Acta. Math. Sin.-English Ser. 37, 775–804 (2021). https://doi.org/10.1007/s10114-020-9328-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-020-9328-y