Trace class criteria for bilinear Hankel forms of higher weights
HTML articles powered by AMS MathViewer
- by Marcus Sundhäll PDF
- Proc. Amer. Math. Soc. 135 (2007), 1377-1388 Request permission
Abstract:
In this paper we give a complete characterization of higher weight Hankel forms, on the unit ball of $\mathbb {C}^d$, of Schatten-von Neumann class $\mathcal {S}_p$, $1\leq p\leq \infty$. For this purpose we give an atomic decomposition for certain Besov-type spaces. The main result is then obtained by combining the decomposition and our earlier results.References
- Sarah H. Ferguson and Richard Rochberg, Higher order Hilbert-Schmidt Hankel forms and tensors of analytic kernels, Math. Scand. 96 (2005), no. 1, 117–146. MR 2142876, DOI 10.7146/math.scand.a-14948
- Haakan Hedenmalm, Boris Korenblum, and Kehe Zhu, Theory of Bergman spaces, Graduate Texts in Mathematics, vol. 199, Springer-Verlag, New York, 2000. MR 1758653, DOI 10.1007/978-1-4612-0497-8
- Svante Janson and Jaak Peetre, A new generalization of Hankel operators (the case of higher weights), Math. Nachr. 132 (1987), 313–328. MR 910059, DOI 10.1002/mana.19871320121
- Svante Janson, Jaak Peetre, and Richard Rochberg, Hankel forms and the Fock space, Rev. Mat. Iberoamericana 3 (1987), no. 1, 61–138. MR 1008445, DOI 10.4171/RMI/46
- O. Loos, Bounded symmetric domains and Jordan pairs, The University of California at Irvine, 1977.
- Jaak Peetre, Hankel kernels of higher weight for the ball, Nagoya Math. J. 130 (1993), 183–192. MR 1223736, DOI 10.1017/S0027763000004499
- Jaak Peetre, Hankel forms of arbitrary weight over a symmetric domain via the transvectant, Rocky Mountain J. Math. 24 (1994), no. 3, 1065–1085. MR 1307592, DOI 10.1216/rmjm/1181072389
- Vladimir V. Peller, Hankel operators and their applications, Springer Monographs in Mathematics, Springer-Verlag, New York, 2003. MR 1949210, DOI 10.1007/978-0-387-21681-2
- Vladimir V. Peller, Vectorial Hankel operators, commutators and related operators of the Schatten-von Neumann class $\gamma _{p}$, Integral Equations Operator Theory 5 (1982), no. 2, 244–272. MR 647702, DOI 10.1007/BF01694041
- Lizhong Peng and Genkai Zhang, Tensor products of holomorphic representations and bilinear differential operators, J. Funct. Anal. 210 (2004), no. 1, 171–192. MR 2052118, DOI 10.1016/j.jfa.2003.09.006
- Michael Reed and Barry Simon, Methods of modern mathematical physics. I, 2nd ed., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. Functional analysis. MR 751959
- Hjalmar Rosengren, Multilinear Hankel forms of higher order and orthogonal polynomials, Math. Scand. 82 (1998), no. 1, 53–88. MR 1634657, DOI 10.7146/math.scand.a-13825
- Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594, DOI 10.1007/978-1-4613-8098-6
- Barry Simon, Trace ideals and their applications, London Mathematical Society Lecture Note Series, vol. 35, Cambridge University Press, Cambridge-New York, 1979. MR 541149, DOI 10.1007/BFb0064579
- M. Sundhäll, Schatten-von Neumann properties of bilinear Hankel forms of higher weights, Math. Scand. 98 (2006), 283-319.
- Gen Kai Zhang, Ha-plitz operators between Moebius invariant subspaces, Math. Scand. 71 (1992), no. 1, 69–84. MR 1216104, DOI 10.7146/math.scand.a-12411
Additional Information
- Marcus Sundhäll
- Affiliation: Department of Mathematics, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Sweden
- Email: sundhall@math.chalmers.se
- Received by editor(s): September 26, 2005
- Received by editor(s) in revised form: November 22, 2005
- Published electronically: October 18, 2006
- Additional Notes: This work is part of the author’s ongoing Ph.D. thesis under the supervision of Yang Liu and Genkai Zhang. He would like to thank Örebro University for the financial support.
- Communicated by: Joseph A. Ball
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1377-1388
- MSC (2000): Primary 32A25, 32A36, 32A37, 47B32, 47B35
- DOI: https://doi.org/10.1090/S0002-9939-06-08583-2
- MathSciNet review: 2276646