Remarks on Nehari's problem, matrix $A_2$ condition, and weighted bounded mean oscillation
| dc.creator | Volberg, A. | |
| dc.creator | Yuditskii, P. | |
| dc.date | 2008-03-15 | |
| dc.date.accessioned | 2026-07-07T09:27:03Z | |
| dc.date.available | 2026-07-07T09:27:03Z | |
| dc.description | We consider Nehari's problem in the case of non-uniqueness of solution. The solution set is then parametrized by the unit ball of $H^{\infty}$ by means of so-called {\em regular generators} -- bounded holomorphic functions $ϕ$. The definition of {\em regularity} is given below, but let us mention now that 1) the following assumption on modulus of $ϕ$ is sufficient for {\em regularity}: $\frac{1}{1-|ϕ|^2}\in L^1(\mathbb{T})$; 2) there is no necessary and sufficient condition of {\em regularity} on bounded holomorphic $ϕ$ in terms of $|ϕ|$ on $\mathbb{T}$, \cite{Kh1}. This makes reasonable the attempt to find a weaker sufficient condition on $|ϕ|$ than the condition in 1). This is done here. Also we are discussing certain new necessary and sufficient conditions of {\em regularity} in terms of bounded mean (weighted) oscillations of $ϕ$. They involve the matrix $A_2$ condition from \cite{TV}. | |
| dc.identifier | https://arxiv.org/abs/0803.2245 | |
| dc.identifier | http://arxiv.org/abs/0803.2245 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156964 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 42C05, 42C20, 42A50, 47B38 | |
| dc.title | Remarks on Nehari's problem, matrix $A_2$ condition, and weighted bounded mean oscillation | |
| dc.type | text |