Abstract
We study big Hankel operators acting on vector-valued Fock spaces with radial weights in \(\mathbb {C}^d\). We provide complete characterizations for the boundedness, compactness and Schatten class membership of such operators.
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Aleman, A., Constantin, O.: Hankel operators on Bergman spaces and similarity to contractions. Int. Math. Res. Not. 2004(35), 1785–1801 (2004)
Aleman, A., Perfekt, K.M.: Hankel forms and embedding theorems in weighted Dirichlet spaces. Int. Math. Res. Not. IMRN 2012(19), 4435–4448 (2012)
Bauer, W.: Mean oscillation and Hankel operators on the Segal–Bargmann space. Integral Equ. Oper. Theory 52, 1–15 (2005)
Bauer, W.: Hilbert–Schmidt Hankel operators on the Segal–Bargmann space. Proc. Am. Math. Soc. 132, 2989–2996 (2004)
Békollé, D., Berger, C.A., Coburn, L.A., Zhu, K.: BMO in the Bergman metric on bounded symmetric domains. J. Funct. Anal. 93, 310–350 (1990)
Bergh, J., Löfström, J.: Interpolation Spaces. An Introduction. Springer, Berlin-New York (1976)
Berndtsson, B., Charpentier, P.: A Sobolev mapping property of the Bergman kernel. Math. Z. 235, 1–10 (2000)
Bommier-Hato, H., Youssfi, E.-H.: Hankel operators and the Stieltjes moment problem. J. Funct. Anal. 258, 978–998 (2010)
Constantin, O., Ortega-Cerdà, J.: Some spectral properties of the canonical solution operator to \({\bar{\partial }}\) on weighted Fock spaces. J. Math. Anal. Appl. 377, 353–361 (2011)
Gohberg, I.C., Krein, M.G.: Introduction to the Theory of Linear Nonselfadjoint Operators. Transl. Math. Monogr. American Mathematical Society, Providence (1969)
Grafakos, L.: Classical Fourier analysis. Graduate Texts in Mathematics, vol. 249. Springer, New York (2014)
Lin, P., Rochberg, R.: Hankel operators on the weighted Bergman spaces with exponential type weights. Integral Equ. Oper. Theory 21(4), 460–483 (1995)
Peller, V.: Hankel Operators and Their Applications. Springer Monographs in Mathematics. Springer, New York (2003)
Seip, K., Youssfi, E.-H.: Hankel operators on Fock spaces and related Bergman kernel estimates. J. Geom. Anal. 23, 170–201 (2013)
Talagrand, M.: Pettis integral and measure theory. Mem. Amer. Math. Soc. 51(307), 224 (1984)
Timoney, R.M.: Bloch functions in several complex variables. I. Bull. Lond. Math. Soc. 12(4), 241–267 (1980)
Timoney, R.M.: M. Bloch functions in several complex variables. II. J. Reine Angew. Math. 319, 1–22 (1980)
Wang, X., Cao, G., Zhu, K.: BMO and Hankel operators on Fock-type spaces. J. Geom. Anal. 25(3), 1650–1665 (2015)
Zhu, K.: Spaces of holomorphic functions in the unit ball. Springer, New York (2005)
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The authors were supported by the FWF project P 30251-N35.
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Bommier-Hato, H., Constantin, O. Big Hankel Operators on Vector-Valued Fock Spaces in \(\mathbb {C}^d\). Integr. Equ. Oper. Theory 90, 2 (2018). https://doi.org/10.1007/s00020-018-2433-y
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DOI: https://doi.org/10.1007/s00020-018-2433-y