Toeplitz operators and weighted norm inequalities on the bidisc
Let \(m\) be the normalized Lebesgue measure on the torus \(T^2\) and let \(L^p=L^p(T^2, m),1\leq p \leq \infty\), denote the Lebesgue space on \(T^2\), and let \(H^p=H^p(T^2, m)=\{f\in L^p, \widehat{f} (\ell, n)=0\) if \(\ell<0\) or \(n<0\}\), \(1<p<\infty\), be the Hardy space on the bidisc respectively. The author studies the Hankel \(H_\varphi\) and Toeplitz \(T_\varphi\) operators on \(H^p\) with \(\varphi\in H^\infty\). He gives two-sided estimates for norm of \(H_\varphi\) and considers the invertibility problem for \(T_\varphi\) using the weighted norm inequalities.
scientific article; zbMATH DE number 1654988