Article
Full entry | Fulltext not available
(moving wall
24 months)
Feedback
Keywords:
Forelli-Rudin type; generalized Hartogs triangle; $L^p$-boundedness
Forelli-Rudin type; generalized Hartogs triangle; $L^p$-boundedness
Summary:
We study a Forelli-Rudin type operator on a generalized Hartogs triangle defined by $$ H^k_n=\{z\in \mathbb C^n\colon |z_1|^2+\cdots +|z_k|^2<|z_{k+1}|^2<|z_{k+2}|^2<\cdots <|z_{n}|^2<1\}, $$ where $z=(z_1, \cdots , z_n)$, $n\geq k+2$ and $k, n\in \mathbb N$. We give a sufficient and necessary condition for the $L^p$-boundedness of the Forelli-Rudin type operators on $H^k_n$.
References:
[1] Bi, E., Hou, Z.: Canonical metrics on generalized Hartogs triangles. C. R., Math., Acad. Sci. Paris 360 (2022), 305-313. DOI 10.5802/crmath.283 | MR 4415724 | Zbl 1487.32127
[2] Bi, E., Su, G.: Balanced metrics and Berezin quantization on Hartogs triangles. Ann. Mat. Pura Appl. (4) 200 (2021), 273-285. DOI 10.1007/s10231-020-00995-2 | MR 4208091 | Zbl 1462.32008
[3] Chakrabarti, D., Shaw, M.-C.: Sobolev regularity of the $\bar{\partial}$-equation on the Hartogs triangle. Math. Ann. 356 (2013), 241-258. DOI 10.1007/s00208-012-0840-y | MR 3038129 | Zbl 1276.32027
[4] Chakrabarti, D., Zeytuncu, Y. E.: $L^p$ mapping properties of the Bergman projection on the Hartogs triangle. Proc. Am. Math. Soc. 144 (2016), 1643-1653. DOI 10.1090/proc/12820 | MR 3451240 | Zbl 1341.32006
[5] Chen, L.: The $L^p$ boundedness of the Bergman projection for a class of bounded Hartogs domains. J. Math. Anal. Appl. 448 (2017), 598-610. DOI 10.1016/j.jmaa.2016.11.024 | MR 3579901 | Zbl 1361.32005
[6] Chen, L.: Weighted Bergman projections on the Hartogs triangle. J. Math. Anal. Appl. 446 (2017), 546-567. DOI 10.1016/j.jmaa.2016.08.065 | MR 3554743 | Zbl 1355.32005
[7] Chen, L., Krantz, S. G., Yuan, Y.: $L^p$ regularity of the Bergman projection on domain covered by the polydisk. J. Funct. Anal. 279 (2020), Article ID 108522, 20 pages. DOI 10.1016/j.jfa.2020.108522 | MR 4088498 | Zbl 1457.32003
[8] Chen, L., McNeal, J. D.: A solution operator for $\bar{\partial}$ on the Hartogs triangle and $L^p$ estimates. Math. Ann. 376 (2020), 407-430. DOI 10.1007/s00208-018-1778-5 | MR 4055165 | Zbl 1439.32098
[9] Edholm, L. D., McNeal, J. D.: The Bergman projection on fat Hartogs triangles: $L^p$ boundedness. Proc. Am. Math. Soc. 144 (2016), 2185-2196. DOI 10.1090/proc/12878 | MR 3460177 | Zbl 1337.32010
[10] Forelli, F., Rudin, W.: Projections on spaces of holomorphic function in balls. Indiana Univ. Math. J. 24 (1974), 593-602. DOI 10.1512/iumj.1974.24.24044 | MR 0357866 | Zbl 0297.47041
[11] Huo, Z., Wick, B. D.: Weighted estimates for the Bergman projection on the Hartogs triangle. J. Funct. Anal. 279 (2020), Article ID 108727, 33 pages. DOI 10.1016/j.jfa.2020.108727 | MR 4134894 | Zbl 1453.32003
[12] Kures, O., Zhu, K.: A class of integral operators on the unit ball of $\Bbb{C}^n$. Integral Equations Oper. Theory 56 (2006), 71-82. DOI 10.1007/s00020-005-1411-3 | MR 2256998 | Zbl 1109.47041
[13] Zhang, S.: Carleson measures on the generalized Hartogs triangles. J. Math. Anal. Appl. 510 (2022), Article ID 126027, 17 pages. DOI 10.1016/j.jmaa.2022.126027 | MR 4372157 | Zbl 1487.32029
[14] Zhao, R.: Generalization of Schur's test and its application to a class of integral operators on the unit ball of $\Bbb{C}^n$. Integral Equations Oper. Theory 82 (2015), 519-532. DOI 10.1007/s00020-014-2215-0 | MR 3369311 | Zbl 1319.47041
[15] Zhao, R., Zhou, L.: $L^{p}$-$L^q$ boundedness of Forelli-Rudin type operators on the unit ball of $\Bbb{C}^n$. J. Funct. Anal. 282 (2022), Article ID 109345, 26 pages. DOI 10.1016/j.jfa.2021.109345 | MR 4354858 | Zbl 1539.47078
[16] Zhu, E., Zou, Q.: $L^{p}$-$L^q$ regularity of Forelli-Rudin-type operators on some bounded Hartogs domains. Math. Nachr. 298 (2025), 2986-3006. DOI 10.1002/mana.12034 | MR 4959157 | Zbl 08110428
[17] Zhu, K.: Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics 226. Springer, New York (2005). DOI 10.1007/0-387-27539-8 | MR 2115155 | Zbl 1067.32005
[18] Zou, Q.: A note on the Berezin transform on the generalized Hartogs triangles. Arch. Math. 122 (2024), 531-540. DOI 10.1007/s00013-024-01971-5 | MR 4734566 | Zbl 1537.32078
[19] Zou, Q.: $L^p$-boundedness of the Berezin transform on generalised Hartogs triangles. Bull. Aust. Math. Soc. 111 (2025), 541-551. DOI 10.1017/S0004972724000674 | MR 4903221 | Zbl 08061419
Search
Partner of
