Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on complete pseudoconvex Reinhardt domains

Συγγραφείς: Çelik, Mehmet, Zeytuncu, Yunus E.

Θεματικοί όροι: keyword:canonical solution operator for $\overline {\partial }$-problem, keyword:Hankel operator, keyword:Hilbert-Schmidt operator, msc:32A36, msc:47B10, msc:47B35

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Relation: mr:MR3633007; zbl:Zbl 06738513; reference:[1] Arazy, J.: Boundedness and compactness of generalized Hankel operators on bounded symmetric domains.J. Funct. Anal. 137 (1996), 97-151. Zbl 0880.47015, MR 1383014, 10.1006/jfan.1996.0042; reference:[2] Arazy, J., Fisher, S. D., Peetre, J.: Hankel operators on weighted Bergman spaces.Am. J. Math. 110 (1988), 989-1053. Zbl 0669.47017, MR 0970119, 10.2307/2374685; reference:[3] Çelik, M., Zeytuncu, Y. E.: Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on complex ellipsoids.Integral Equations Oper. Theory 76 (2013), 589-599. Zbl 1288.47028, MR 3073947, 10.1007/s00020-013-2070-4; reference:[4] Harrington, P., Raich, A.: Defining functions for unbounded $C^m$ domains.Rev. Mat. Iberoam. 29 (2013), 1405-1420. Zbl 1288.26008, MR 3148609, 10.4171/RMI/762; reference:[5] Harrington, P. S., Raich, A.: Sobolev spaces and elliptic theory on unbounded domains in $\mathbb R^n$.Adv. Diff. Equ. 19 (2014), 635-692. Zbl 1301.46015, MR 3252898; reference:[6] Krantz, S. G., Li, S.-Y., Rochberg, R.: The effect of boundary geometry on Hankel operators belonging to the trace ideals of Bergman spaces.Integral Equations Oper. Theory 28 (1997), 196-213. Zbl 0903.47019, MR 1451501, 10.1007/BF01191818; reference:[7] Le, T.: Hilbert-Schmidt Hankel operators over complete Reinhardt domains.Integral Equations Oper. Theory 78 (2014), 515-522. Zbl 1318.47047, MR 3180876, 10.1007/s00020-013-2103-z; reference:[8] Li, H.: Schatten class Hankel operators on the Bergman spaces of strongly pseudoconvex domains.Proc. Am. Math. Soc. 119 (1993), 1211-1221. Zbl 0802.47022, MR 1169879, 10.2307/2159984; reference:[9] Peloso, M. M.: Hankel operators on weighted Bergman spaces on strongly pseudoconvex domains.Ill. J. Math. 38 (1994), 223-249. Zbl 0812.47023, MR 1260841, 10.1215/ijm/1255986798; reference:[10] Retherford, J. R.: Hilbert space: Compact operators and the trace theorem.London Mathematical Society Student Texts 27, Cambridge University Press, Cambridge (1993). Zbl 0783.47031, MR 1237405; reference:[11] Schneider, G.: A different proof for the non-existence of Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on the Bergman space.Aust. J. Math. Anal. Appl. (electronic only) 4 (2007), Artical No. 1, pages 7. Zbl 1220.47040, MR 2326997; reference:[12] Wiegerinck, J. J. O. O.: Domains with finite-dimensional Bergman space.Math. Z. 187 (1984), 559-562. Zbl 0534.32001, MR 0760055, 10.1007/BF01174190; reference:[13] Zhu, K. H.: Hilbert-Schmidt Hankel operators on the Bergman space.Proc. Am. Math. Soc. 109 (1990), 721-730. Zbl 0731.47028, MR 1013987, 10.2307/2048212

Διαθεσιμότητα: http://hdl.handle.net/10338.dmlcz/146049

Compactness of the \(\overline{\partial}\)-Neumann problem on convex domains

Συγγραφείς: Fu, Siqi, Straube, Emil J.

Θεματικοί όροι: \((0,q)\)-forms, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, \(\overline\partial\)-Neumann operator, bounded convex domain, solution operator for \(\overline\partial\)-problem

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Σύνδεσμος πρόσβασης: https://zbmath.org/1268059