zbMATH — the first resource for mathematics

The effect of boundary geometry on Hankel operators belonging to the trace ideals of Bergman spaces. (English) Zbl 0903.47019
Summary: The characterization of those \(f\) for which the Hankel operators \(H_f\) belong to various trace ideals over Bergman spaces on pseudoconvex domains of finite type in complex dimension two is given. In particular, we determine how the cutoff values are affected by the boundary geometry.

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47B38 Linear operators on function spaces (general)
Full Text: DOI
[1] [AFP1] J. Arazy, S. Fisher, and J. Peetre, Hankel operators on weighted Bergman spaces,Amer. J. Math. 111 (1988), 989-1054. · Zbl 0669.47017
[2] [AFP2] J. Arazy, S. Fisher, S. Janson and J. Peetre, Hankel operators on planar domains,Constructive Approximation 6(1990), 113-138. · Zbl 0703.47019
[3] [AFJP] J. Arazy, S. Fisher, S. Janson and J. Peetre, Membership of Hankel operators on the unit ball in unitary ideals.J. London Math. Soc. 43(1991), 485-508. · Zbl 0747.47019
[4] [BL1] F. Beatrous and Song-Ying Yi, On the boundedness and compactness of operators of Hankel type,Jour. of Funct. Anal. 111(1993), 350-379. · Zbl 0793.47022
[5] [BL2] Beatrous, F., S.-Y. Li, Trace ideal criteria for operators of Hankel type,Illinois J. Math. 39(1995), 723-754. · Zbl 0846.47020
[6] [BBCZ] D. B?koll?, C. A. Berger, L. A. Coburn, and K. H. Zhu,BMO in the Bergman metric on bounded symmetric domains,J. Funct. Anal. 93(1990), 310-350. · Zbl 0765.32005
[7] [CAT] D. Catlin, Estimates of invariant metrics on pseudoconvex domains of dimension two,Math. Z. 200(1989), 429-466. · Zbl 0661.32030
[8] [CS] M. Cotlar and C. Sadosky, Abstract, Weighted, and Multidimensional Adamjan-Aronov-Krein Theorems and Singular Number of Sarason Commutants,Int. Equations and Op. Thy. 17(1993), 171-200. · Zbl 0804.47026
[9] [FR] M. Feldman and R. Rochberg, Singular value estimates for commutators and Hankel operators on the unit ball and Heisenberg group,Analysis and P.D.E., Lecture Notes in Pure and Applied Math. 122, Decker, New York, 1990. · Zbl 0703.47020
[10] [J] S. Janson, Hankel operators between weighted Bergman spaces,Ark. Math. 26(1988), 205-219. · Zbl 0676.47013
[11] [K] S. G. Krantz,Function Theory of Several Complex Variables, 2nd Ed., Wadsworth, Belmont, 1992. · Zbl 0776.32001
[12] [KL1] S. G. Krantz and S-Y. Li, On the decomposition theorems for Hardy spaces and applications in domains in ? n ,J. of Fourier Analysis and Applications 2(1995), 65-107. · Zbl 0886.32003
[13] [KL2] S. G. Krantz and S-Y. Li, A Note on Hardy spaces and functions of bounded mean oscillation on domains in ? n ,Michigan J. of Math 41(1994), 51-72. · Zbl 0802.32013
[14] [KL3] S. G. Krantz and S-Y. Li, Duality theorems for Hardy and Bergman spaces on convex domains of finite type in ? n ,Ann. of Fourier Institute 45(1995), 1305-1327. · Zbl 0835.32004
[15] [L] H. Li, Schatten Class Hankel Operators on Bergman Space of Strongly Pseudoconvex Domain,IEOPT, 1995.
[16] [MCN1] J. McNeal, Boundary behavior of the Bergman kernel function in ?2,Duke Math. J. 58(1989), 499-512. · Zbl 0675.32020
[17] [MCN2] J. McNeal, Estimates on the Bergman kernels of convex domains,Advances in Math. 109(1994), 108-139. · Zbl 0816.32018
[18] [MS] J. D. McNeal and E. M. Stein, Mapping properties of the Bergman projection on convex domains of finite type,Duke Math. J. 73(1994), 177-199. · Zbl 0801.32008
[19] [NRSW] A. Nagel, Rosay, E. M. Stein and Wainger, Estimates for the Bergman and Szeg? kernels in ?2,Ann. of Math. 129(1989), 113-149. · Zbl 0667.32016
[20] [Pe] V. V. Peller, Hankel operators of classS p and applications,Mat. Sb. 113(1980), 538-581. · Zbl 0458.47022
[21] [P] M. Peloso, Hankel operators on weighted Bergman spaces on strongly pseudoconvex domains,Ill. J. of Math. 38(1994), 223-249. · Zbl 0812.47023
[22] [W] R. Wallst?n, Hankel operators between Bergman spaces in the ball,Ark. Math. 28(1990), 183-192. · Zbl 0705.47023
[23] [Zh] D. Zheng, Schatten class Hankel operators on Bergman spaces,Int. Equations and Op. Thy. 13(1990), 442-459. · Zbl 0729.47023
[24] [Z] Kehe Zhu, Schatten class Hankel operators on the Bergman space of the unit ball,Amer. J. Math. 113(1991), 147-167. · Zbl 0734.47017
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.