Hankel and Toeplitz transforms on H 1: continuity, compactness and Fredholm properties
Papadimitrakis, M. and Virtanen, J. A. (2008) Hankel and Toeplitz transforms on H 1: continuity, compactness and Fredholm properties. Integral Equations and Operator Theory, 61 (4). pp. 573-591. ISSN 0378-620X
To link to this article DOI: 10.1007/s00020-008-1609-2
We revisit the boundedness of Hankel and Toeplitz operators acting on the Hardy space H 1 and give a new proof of the old result stating that the Hankel operator H a is bounded if and only if a has bounded logarithmic mean oscillation. We also establish a sufficient and necessary condition for H a to be compact on H 1. The Fredholm properties of Toeplitz operators on H 1 are studied for symbols in a Banach algebra similar to C + H ∞ under mild additional conditions caused by the differences in the boundedness of Toeplitz operators acting on H 1 and H 2.