In this article, we solve completely Gleason's problem on Fock-Sobolev spaces $F^{p,m}$ for any non-negative integer $m$ and $0 < p\leq\infty$.
Jineng DAI
,
Jingyun ZHOU
. GLEASON'S PROBLEM ON FOCK-SOBOLEV SPACES[J]. Acta mathematica scientia, Series B, 2021
, 41(1)
: 337
-348
.
DOI: 10.1007/s10473-021-0120-6
[1] Bargmann V. On a Hilbert space of analytic functions and an associated integral transform. Comm Pure Appl Math, 1961, 14:187-214
[2] Janson S, Peetre J, Rochberg R. Hankel forms and the Fock space. Revista Mat Iberoamer, 1987, 3:61-138
[3] Carswell B, MacCluer B, Schuster A. Composition operators on the Fock space. Acta Sci Math (Szeged), 2003, 69:871-887
[4] Cho H, Zhu K. Fock-Sobolev spaces and their Carleson measures. J Funct Anal, 2012, 263:2483-2506
[5] Zhu K. Analysis on Fock Spaces. New York:Springer-Verlag, 2012
[6] Hu Z. Equivalenct norms on Fock spaces with some application to extended Cesaro operators. Proc Amer Math Soc, 2013, 141:2829-2840
[7] Dai J, Wang B. A class of integral operators and the Fock space. Complex Var Elliptic Equ, 2016, 61:562-573
[8] Rudin W. Function Theory in the Unit Ball of Cn. New York:Springer-Verlag, 1980
[9] Kerzman K, Nagal A. Finitely generated ideals in certain function algebras. J Funct Anal, 1971, 7:212-215
[10] Ahern P, Schneider R. Holomorphic Lipschitz functions in pseudoconvex domains. Amer J Math, 1979, 101:543-565
[11] Zhu K. The Bergman spaces, the Bloch space and Gleason's problem. Trans Amer Math Soc, 1988, 309:253-268
[12] Ortega J. The gleason problem in Bergman-Sobolev spaces. Complex Var Elliptic Equ, 1992, 20:157-170
[13] Hu Z. Gleason's problem for harmonic mixed norm and Bloch spaces in convex domains. Math Nachr, 2006, 279:164-178
[14] Zhang X, Li M, Guan Y. The equivalent norms and the Gleason's problem on μ-Zygmund spaces in Cn. J Math Anal Appl, 2014, 419:185-199
[15] Zhu K. Spaces of Holomorphic Functions in the Unit Ball. New York:Springer-Verlag, 2005
