Korenblum constants for some function spaces
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- by Wee JunJie and Le Hai Khoi PDF
- Proc. Amer. Math. Soc. 148 (2020), 1175-1185 Request permission
Abstract:
We study the Korenblum Maximum Principle on the weighted Fock spaces and the weighted Bergman spaces with exponential weights. First, we give explicit expressions for the upper bounds of Korenblum constants for the weighted Fock spaces. Then, we obtain upper bounds of such constants for the weighted Bergman spaces. Finally, we show a failure of the Korenblum Maximum Principle for weighted Bergman spaces $A^p_\alpha (\mathbb {D})$, where $0<p<1$, $\alpha >0$.References
- Vladimir Božin and Boban Karapetrović, Failure of Korenblum’s maximum principle in Bergman spaces with small exponents, Proc. Amer. Math. Soc. 146 (2018), no. 6, 2577–2584. MR 3778159, DOI 10.1090/proc/13946
- N. Danikas and W. K. Hayman, Domination on sets and in $H^p$, Results Math. 34 (1998), no. 1-2, 85–90. Dedicated to Paul Leo Butzer. MR 1635585, DOI 10.1007/BF03322039
- Walter Kurt Hayman, On a conjecture of Korenblum, Analysis (Munich) 19 (1999), no. 2, 195–205. MR 1705360, DOI 10.1524/anly.1999.19.2.195
- A. Hinkkanen, On a maximum principle in Bergman space, J. Anal. Math. 79 (1999), 335–344. MR 1749317, DOI 10.1007/BF02788246
- Jianhui Hu and Zengjian Lou, The Korenblum’s maximum principle in Fock spaces with small exponents, J. Math. Anal. Appl. 470 (2019), no. 2, 770–776. MR 3870588, DOI 10.1016/j.jmaa.2018.10.029
- Boris Korenblum, A maximum principle for the Bergman space, Publ. Mat. 35 (1991), no. 2, 479–486. MR 1201570, DOI 10.5565/PUBLMAT_{3}5291_{1}2
- Boris Korenblum and Kendall Richards, Majorization and domination in the Bergman space, Proc. Amer. Math. Soc. 117 (1993), no. 1, 153–158. MR 1113643, DOI 10.1090/S0002-9939-1993-1113643-3
- B. Korenblum, R. O’Neil, K. Richards, and K. Zhu, Totally monotone functions with applications to the Bergman space, Trans. Amer. Math. Soc. 337 (1993), no. 2, 795–806. MR 1118827, DOI 10.1090/S0002-9947-1993-1118827-0
- Jerk Matero, On Korenblum’s maximum principle for the Bergman space, Arch. Math. (Basel) 64 (1995), no. 4, 337–340. MR 1319004, DOI 10.1007/BF01198089
- Alexander Schuster, The maximum principle for the Bergman space and the Möbius pseudodistance for the annulus, Proc. Amer. Math. Soc. 134 (2006), no. 12, 3525–3530. MR 2240664, DOI 10.1090/S0002-9939-06-08378-X
- Wilhelm Schwick, On Korenblum’s maximum principle, Proc. Amer. Math. Soc. 125 (1997), no. 9, 2581–2587. MR 1307563, DOI 10.1090/S0002-9939-97-03247-4
- Chunjie Wang, Refining the constant in a maximum principle for the Bergman space, Proc. Amer. Math. Soc. 132 (2004), no. 3, 853–855. MR 2019965, DOI 10.1090/S0002-9939-03-07137-5
- Chunjie Wang, An upper bound on Korenblum’s constant, Integral Equations Operator Theory 49 (2004), no. 4, 561–563. MR 2091477, DOI 10.1007/s00020-004-1310-z
- Chunjie Wang, On Korenblum’s constant, J. Math. Anal. Appl. 296 (2004), no. 1, 262–264. MR 2070507, DOI 10.1016/j.jmaa.2004.04.012
- Chunjie Wang, On Korenblum’s maximum principle, Proc. Amer. Math. Soc. 134 (2006), no. 7, 2061–2066. MR 2215775, DOI 10.1090/S0002-9939-06-08311-0
- Chunjie Wang, Behavior of the constant in Korenblum’s maximum principle, Math. Nachr. 281 (2008), no. 3, 447–454. MR 2392127, DOI 10.1002/mana.200510616
- Chunjie Wang, Some results on Korenblum’s maximum principle, J. Math. Anal. Appl. 373 (2011), no. 2, 393–398. MR 2720689, DOI 10.1016/j.jmaa.2010.07.052
- Kehe Zhu, Analysis on Fock spaces, Graduate Texts in Mathematics, vol. 263, Springer, New York, 2012. MR 2934601, DOI 10.1007/978-1-4419-8801-0
Additional Information
- Wee JunJie
- Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore
- ORCID: 0000-0001-8444-3252
- Email: weej0016@e.ntu.edu.sg
- Le Hai Khoi
- Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore
- MR Author ID: 262091
- Email: lhkhoi@ntu.edu.sg
- Received by editor(s): May 1, 2019
- Received by editor(s) in revised form: July 18, 2019
- Published electronically: September 23, 2019
- Additional Notes: This work was supported in part by MOE’s AcRF Tier 1 grant M4011724.110 (RG128/16)
- Communicated by: Stephan Ramon Garcia
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1175-1185
- MSC (2010): Primary 30H20, 46E15
- DOI: https://doi.org/10.1090/proc/14778
- MathSciNet review: 4055945