Two remarks on the relationship between BMO-regularity and analytic stability of interpolation for lattices of measurable functions

The subject-matter of this paper is Hardy type spaces on the measure space $(\mathbb T,m)\times(\Omega,\mu)$, where $(\mathbb T,m)$ is the unit circle with Lebesgue measure. There is a characterization of analytic stability for real interpolation of weighted Hardy spaces on $\mathbb T\times\Omega$ a complete proof of which was present in the literature only for the case where $\mu$ is a point mass. Here this gap is filled and the proof of the general case is presented. Next, in previous work by S. Kislyakov, certain results concerning BMO-regular lattices on $(\mathbb T\times\Omega,m\times\mu)$ were proved under the assumption that the measure $\mu$ is discrete. Here this extraneous assumption is lifted. Bibl. – 9 titles.