Embedding of 𝒬_{𝓅} into tent spaces

Lv, Xiaofen

doi:10.1090/proc/16758

Embedding of $\mathcal {Q}_p$ into tent spaces
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by Xiaofen Lv;

Proc. Amer. Math. Soc. 152 (2024), 2893-2903

DOI: https://doi.org/10.1090/proc/16758

Published electronically: May 7, 2024

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Abstract:

In this paper, we prove embedding theorems for the Möbius invariant space $\mathcal {Q}_p$ on the open unit ball of $\mathbb {C}^n$ into logarithmic tent spaces in the Bergman metric.

References

J. Arazy, S. D. Fisher, and J. Peetre, Möbius invariant function spaces, J. Reine Angew. Math. 363 (1985), 110–145. MR 814017, DOI 10.1007/BFb0078341
Rauno Aulaskari, David A. Stegenga, and Jie Xiao, Some subclasses of BMOA and their characterization in terms of Carleson measures, Rocky Mountain J. Math. 26 (1996), no. 2, 485–506. MR 1406492, DOI 10.1216/rmjm/1181072070
Rauno Aulaskari, Jie Xiao, and Ru Han Zhao, On subspaces and subsets of BMOA and UBC, Analysis 15 (1995), no. 2, 101–121. MR 1344246, DOI 10.1524/anly.1995.15.2.101
Guanlong Bao, Javad Mashreghi, Stamatis Pouliasis, and Hasi Wulan, Möbius invariant function spaces and Dirichlet spaces with superharmonic weights, J. Aust. Math. Soc. 106 (2019), no. 1, 1–18. MR 3897398, DOI 10.1017/S1446788718000022
Lennart Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921–930. MR 117349, DOI 10.2307/2372840
Lennart Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547–559. MR 141789, DOI 10.2307/1970375
Joseph A. Cima and Warren R. Wogen, A Carleson measure theorem for the Bergman space on the ball, J. Operator Theory 7 (1982), no. 1, 157–165. MR 650200
John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
William W. Hastings, A Carleson measure theorem for Bergman spaces, Proc. Amer. Math. Soc. 52 (1975), 237–241. MR 374886, DOI 10.1090/S0002-9939-1975-0374886-9
Z. J. Hu, $\mathcal {Q}_p$ spaces in the unit ball of $\mathbb {C}^n$ with $\frac {n-1}{n}<p\leq 1$, J. Huzhou Teach. Coll. 25 (2003), 1–10.
Zhangjian Hu, Xiaofen Lv, and Kehe Zhu, Carleson measures and balayage for Bergman spaces of strongly pseudoconvex domains, Math. Nachr. 289 (2016), no. 10, 1237–1254. MR 3520714, DOI 10.1002/mana.201500021
Xiaofen Lv and Kehe Zhu, Integrability of mean oscillation with applications to Hankel operators, Integral Equations Operator Theory 91 (2019), no. 1, Paper No. 5, 23. MR 3905349, DOI 10.1007/s00020-019-2504-8
Daniel Luecking, A technique for characterizing Carleson measures on Bergman spaces, Proc. Amer. Math. Soc. 87 (1983), no. 4, 656–660. MR 687635, DOI 10.1090/S0002-9939-1983-0687635-6
Daniel H. Luecking, Embedding theorems for spaces of analytic functions via Khinchine’s inequality, Michigan Math. J. 40 (1993), no. 2, 333–358. MR 1226835, DOI 10.1307/mmj/1029004756
Junming Liu, Zengjian Lou, and Kehe Zhu, Embedding of Möbius invariant function spaces into tent spaces, J. Geom. Anal. 27 (2017), no. 2, 1013–1028. MR 3625141, DOI 10.1007/s12220-016-9708-9
Santeri Miihkinen, Jordi Pau, Antti Perälä, and Maofa Wang, Volterra type integration operators from Bergman spaces to Hardy spaces, J. Funct. Anal. 279 (2020), no. 4, 108564, 32. MR 4095802, DOI 10.1016/j.jfa.2020.108564
Caiheng Ouyang, Weisheng Yang, and Ruhan Zhao, Möbius invariant $Q_p$ spaces associated with the Green’s function on the unit ball of $\textbf {C}^n$, Pacific J. Math. 182 (1998), no. 1, 69–99. MR 1610626, DOI 10.2140/pjm.1998.182.69
Marco M. Peloso, Möbius invariant spaces on the unit ball, Michigan Math. J. 39 (1992), no. 3, 509–536. MR 1182505, DOI 10.1307/mmj/1029004604
Jie Xiao, Holomorphic $Q$ classes, Lecture Notes in Mathematics, vol. 1767, Springer-Verlag, Berlin, 2001. MR 1869752, DOI 10.1007/b87877
Jie Xiao, Geometric $Q_p$ functions, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2006. MR 2257688
Jie Xiao, The $\scr Q_p$ Carleson measure problem, Adv. Math. 217 (2008), no. 5, 2075–2088. MR 2388086, DOI 10.1016/j.aim.2007.08.015
Ke He Zhu, Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains, J. Operator Theory 20 (1988), no. 2, 329–357. MR 1004127
Kehe Zhu, Spaces of holomorphic functions in the unit ball, Graduate Texts in Mathematics, vol. 226, Springer-Verlag, New York, 2005. MR 2115155
Kehe Zhu, Operator theory in function spaces, 2nd ed., Mathematical Surveys and Monographs, vol. 138, American Mathematical Society, Providence, RI, 2007. MR 2311536, DOI 10.1090/surv/138