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

D. V. Rutsky

Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 37, Tome 366 (2009), pp. 102-115

Résumé

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.