Factorization of a class of Toeplitz + hankel operators and the A_p-condition

dc.creatorBasor, Estelle L.
dc.creatorEhrhardt, Torsten
dc.date2004-04-20
dc.date.accessioned2026-07-07T05:07:35Z
dc.date.available2026-07-07T05:07:35Z
dc.descriptionLet $M(ϕ)=T(ϕ)+H(ϕ)$ 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.identifierhttps://arxiv.org/abs/math/0404358
dc.identifierhttp://arxiv.org/abs/math/0404358
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70912
dc.subjectFunctional Analysis
dc.subjectClassical Analysis and ODEs
dc.subject47B35: 47G
dc.titleFactorization of a class of Toeplitz + hankel operators and the A_p-condition
dc.typetext

Files

Collections