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We consider Nehari's problem in the case of non-uniqueness of solution. Thesolution set is then parametrized by the unit ball of $H^{\infty}$ by means ofso-called {\em regular generators} -- bounded holomorphic functions $\phi$. Thedefinition of {\em regularity} is given below, but let us mention now that 1)the following assumption on modulus of $\phi$ is sufficient for {\emregularity}: $\frac{1}{1-|\phi|^2}\in L^1(\mathbb{T})$; 2) there is nonecessary and sufficient condition of {\em regularity} on bounded holomorphic$\phi$ in terms of $|\phi|$ on $\mathbb{T}$, \cite{Kh1}. This makes reasonablethe attempt to find a weaker sufficient condition on $|\phi|$ than thecondition in 1). This is done here. Also we are discussing certain newnecessary and sufficient conditions of {\em regularity} in terms of boundedmean (weighted) oscillations of $\phi$. They involve the matrix $A_2$ conditionfrom \cite{TV}.

Remarks on Nehari's problem, matrix $A_2$ condition, and weighted bounded mean oscillation