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 $\phi$. The definition of { \em regularity} is given below, but let us mention now that 1) the following assumption on modulus of $\phi$ is sufficient for { \em regularity}: $\frac{ 1}{ 1-|\phi|^2}\in L^1(\mathbb{ T})$; 2) there is no necessary and sufficient condition of { \em regularity} on bounded holomorphic $\phi$ in terms of $|\phi|$ on $\mathbb{ T}$, \cite{ Kh1}. This makes reasonable the attempt to find a weaker sufficient condition on $|\phi|$ 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 $\phi$. They involve the matrix $A_2$ condition from \cite{ TV}.
Categories: math-ph math.MP