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Toeplitz operators on Bergman spaces and Hardy multipliers. (English) Zbl 1237.47034

The authors study Toeplitz operators with radial symbols in weighted Bergman spaces \(A _ \mu^ p\), \(1<p<\infty\), on the unit disk in the complex plane. The case \(p=2\) was earlier investigated in [S. Grudsky, A. Karapetyants and N. Vasilevski, J. Oper. Theory 49, No. 2, 325–346 (2003; Zbl 1027.32010)]. In the case under consideration, it is proved that the Bergman space can be decomposed into finite-dimensional subspaces spanned by monomials with degrees in certain subintervals of \(\mathbb N\). The boundedness and compactness of a Toeplitz operator is characterized in terms of its behaviour on these blocks.

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
46E15 Banach spaces of continuous, differentiable or analytic functions
32A36 Bergman spaces of functions in several complex variables

Citations:

Zbl 1027.32010
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