Journal
INTEGRAL EQUATIONS AND OPERATOR THEORY
Volume 70, Issue 4, Pages 541-559Publisher
BIRKHAUSER VERLAG AG
DOI: 10.1007/s00020-011-1887-y
Keywords
Toeplitz operator; Fock space; Carleson measure
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Funding
- National Natural Science Foundation of China [10771064]
- Natural Science Foundation of Zhejiang province [Y7080197, Y6090036, Y6100219]
- Foundation of Creative Group in Colleges and Universities of Zhejiang Province [T200924]
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In this paper, we study Toeplitz operators T (mu) from one Fock space F(alpha)(p) to another F(alpha)(q) for 1 < p, q < a with positive Borel measures mu as symbols. We characterize the boundedness (and compactness) of T(mu) : F(alpha)(p) -> F(alpha)(q) in terms of the averaging function (mu) over cap (r) and the t-Berezin transform (mu) over cap (t) respectively. Quite differently from the Bergman space case, we show that T (mu) is bounded (or compact) from F(alpha)(p) for some p <= q if and only if T (mu) is bounded (or compact) from F(alpha)(p) to F(alpha)(q) for all p <= q. In order to prove our main results on T (mu) , we introduce and characterize (vanishing) (p, q)-Fock Carleson measures on C (n) .
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