Toeplitz operators on Dirichlet-Besov spacesPerälä, A., Taskinen, J. and Virtanen, J. (2017) Toeplitz operators on Dirichlet-Besov spaces. Houston Journal of Mathematics, 43 (1). pp. 93-108. ISSN 0362-1588
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. Official URL: https://www.math.uh.edu/~hjm/Electronic-Editions.h... Abstract/SummaryWe study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.
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