Lusky, Wolfgang; Taskinen, Jari Toeplitz operators on Bergman spaces and Hardy multipliers. (English) Zbl 1237.47034 Stud. Math. 204, No. 2, 137-154 (2011). 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. Reviewer: Vladimir S. Pilidi (Rostov-na-Donu) Cited in 10 Documents 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 Keywords:Toeplitz operator; weighted Bergman space; radial symbol; radial weight Citations:Zbl 1027.32010 PDFBibTeX XMLCite \textit{W. Lusky} and \textit{J. Taskinen}, Stud. Math. 204, No. 2, 137--154 (2011; Zbl 1237.47034) Full Text: DOI