Hankel matrices acting on Dirichlet spaces. (English) Zbl 1326.47028
The authors obtain a characterization for the boundedness of the operator induced by the Hankel matrix acting on Dirichlet space \(\mathcal{D}_\alpha\) (within the best possible \(\alpha \in (0, 2)\)) in terms of a \(p\)-Carleson measure supported on \((-1, 1)\), \(0<p<\infty\). An application to the boundedness of the generalized Hilbert operator is also included.
Reviewer: Luis Filipe Pinheiro de Castro (Aveiro)
MSC:
| 47B35 | Toeplitz operators, Hankel operators, Wiener-Hopf operators |
| 31C25 | Dirichlet forms |
| 46E15 | Banach spaces of continuous, differentiable or analytic functions |
| 47B38 | Linear operators on function spaces (general) |
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