Geodesic
On Hankel Forms of Higher Weights: The Case of Hardy Spaces
Canadian journal of mathematics, Tome 62 (2010) no. 2, pp. 439-455

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we study bilinear Hankel forms of higher weights on Hardy spaces in several dimensions. (The Schatten class Hankel forms of higher weights on weighted Bergman spaces have already been studied by Janson and Peetre for one dimension and by Sundhäll for several dimensions). We get a full characterization of Schatten class Hankel forms in terms of conditions for the symbols to be in certain Besov spaces. Also, the Hankel forms are bounded and compact if and only if the symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively.
DOI : 10.4153/CJM-2010-027-8
Mots-clés : 32A25, 32A35, 32A37, 47B35, Hankel forms, Schatten–von Neumann classes, Bergman spaces, Hardy spaces, Besov spaces, transvectants, unitary representations, Möbius group 
Sundhäll, Marcus; Tchoundja, Edgar. On Hankel Forms of Higher Weights: The Case of Hardy Spaces. Canadian journal of mathematics, Tome 62 (2010) no. 2, pp. 439-455. doi: 10.4153/CJM-2010-027-8
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[1] [1] Aleman, A. and Constantin, O., Hankel operators on Bergman spaces and similarity to contractions. Int. Math. Res. Not. 2004, no. 35, 1785–1801. Google Scholar

[2] [2] Beatrous, F. and Burbea, J., Holomorphic Sobolev spaces on the ball. Dissertationes Math. (Rozprawy Mat.) 276(1989). Google Scholar

[3] [3] Burbea, J., Boundary behavior of holomorphic functions in the ball. Pacific J. Math. 127(1987), no. 1, 1–17. Google Scholar

[4] [4] Coifman, R., Rochberg, R., and G.Weiss, Factorization theorems for Hardy spaces in several variables. Ann. of Math. 103(1976), no. 3, 611–635. doi:10.2307/1970954 Google Scholar

[5] [5] Feldman, M. and Rochberg, R., Singular value estimates for commutators and Hankel operators on the unit ball and the Heisenberg group. In: Analysis and Partial Differential Equations. Lecture Notes in Pure and Appl. Math. 122. Dekker, New York, 1990, pp. 121–159. Google Scholar

[6] [6] Janson, S. and Peetre, J., A new generalization of Hankel operators (the case of higher weights). Math. Nachr. 132(1987), 313–328. doi:10.1002/mana.19871320121 Google Scholar

[7] [7] Janson, S., Peetre, J., and Rochberg, R., Hankel forms and the Fock space. Revista Mat. Iberoamericana 3(1987), no. 1, 61-138. Google Scholar

[8] [8] Peller, V. V., Vectorial Hankel operators, commutators and related operators of the Schatten–von Neumann class °p. Integral Equations Operator Theory 5(1982), no. 2, 244–272. doi:10.1007/BF01694041 Google Scholar

[9] [9] Peller, V. V., Hankel operators and their applications. Springer-Verlag, New York, 2003. Google Scholar

[10] [10] Peng, L. and Zhang, G., Tensor products of holomorphic representations and bilinear differential operators. J. Funct. Anal. 210(2004), no. 1, 171–192. doi:10.1016/j.jfa.2003.09.006 Google Scholar

[11] [11] Rochberg, R., Trace ideal criteria for Hankel operators and commutators. Indiana Univ. Math. J. 31(1982), no. 6, 913–925. doi:10.1512/iumj.1982.31.31062 Google Scholar

[12] [12] Rudin, W., The radial variation of analytic functions. Duke Math. J. 22(1955), 235–242. doi:10.1215/S0012-7094-55-02224-9 Google Scholar

[13] [13] Rudin, W., Function Theory in the Unit Ball of Cn. Grundlehren der Mathematischen Wissenschaften 241. Springer-Verlag, New York, 1980. Google Scholar

[14] [14] Sundhäll, M., Schatten-von Neumann properties of bilinear Hankel forms of higher weights. Math. Scand. 98(2006), no. 2, 283–319. Google Scholar

[15] [15] Sundhäll, M., Trace class criteria for bilinear Hankel forms of higher weights. Proc. Amer. Math. Soc. 135(2007), no. 5, 1377–1388. doi:10.1090/S0002-9939-06-08583-2 Google Scholar

[16] [16] Zhang, G., Hankel operators on Hardy spaces and Schatten classes. Chinese Ann. Math. Ser. B, 12(1991), no. 3, 282–294. Google Scholar

[17] [17] Zhao, R. and Zhu, K., Theory of Bergman spaces in the unit ball of Cn. To appear in Mem. Soc. Math. France. Google Scholar

[18] [18] Zhu, K., Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics 226. Springer-Verlag, New York, 2005. Google Scholar

[19] [19] Zhu, K., A class of Möbius invariant function spaces. Illinois J. Math. 51(2007), no. 3, 977–1002. Google Scholar

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