On the action of Hankel and Toeplitz operators on some function spaces
Hardy and Toeplitz operators are usually considered on the (Hilbert) Hardy space \(H^ 2=H^ 2({\mathbb{T}})\), \({\mathbb{T}}\) unit circumference. In this very important paper we consider their action on some other function spaces, especially, \(H^ p\), \(0<p<\infty\) and \({\mathcal B}\) (Bloch space). If \(p=1\), the condition for boundedness on the symbol b of a Hankel operator reads \(\bar Pb\in \bar {\mathcal B}\) (P Riesz projection). We treat further Hankel operators with Bloch symbols. Such operators act from \(B_ p^{0,1}\) into \(B_ p^{0,\infty}\). In the last section the boundedness of Toeplitz symbols is established for a quite general class of spaces.
scientific article; zbMATH DE number 3927704
scientific article