Factorization of a class of Toeplitz + hankel operators and the A_p-condition
| dc.creator | Basor, Estelle L. | |
| dc.creator | Ehrhardt, Torsten | |
| dc.date | 2004-04-20 | |
| dc.date.accessioned | 2026-07-07T05:07:35Z | |
| dc.date.available | 2026-07-07T05:07:35Z | |
| dc.description | Let $M(ϕ)=T(ϕ)+H(ϕ)$ be the Toeplitz plus Hankel operator acting on $H^p(\T)$ with generating function $ϕ\in L^\iy(\T)$. In a previous paper we proved that $M(ϕ)$ is invertible if and only if $ϕ$ admits a factorization $ϕ(t)=ϕ_{-}(t)ϕ_{0}(t)$ such that $ϕ_{-}$ and $ϕ_{0}$ and their inverses belong to certain function spaces and such that a further condition formulated in terms of $ϕ_{-}$ and $ϕ_{0}$ is satisfied. In this paper we prove that this additional condition is equivalent to the Hunt-Muckenhoupt-Wheeden condition (or, $A_{p}$-condition) for a certain function $σ$ defined on $[-1,1]$, which is given in terms of $ϕ_{0}$. As an application, a necessary and sufficient criteria for the invertibility of $M(ϕ)$ with piecewise continuous functions $ϕ$ is proved directly. Fredholm criteria are obtained as well. | |
| dc.identifier | https://arxiv.org/abs/math/0404358 | |
| dc.identifier | http://arxiv.org/abs/math/0404358 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70912 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 47B35: 47G | |
| dc.title | Factorization of a class of Toeplitz + hankel operators and the A_p-condition | |
| dc.type | text |