Speaker
Description
In 1995, N. Kalton discovered that the stability of complex interpolation
$(X_A, Y_A)_\theta = \left[ (X, Y)_\theta \right]_A$ of a couple of Hardy-type spaces for Banach lattices of measurable functions on the unit circle is characterized in terms of the BMO-regularity property of lattice $X’ Y$, that is, the existence of majorants $w$ for arbitrary functions of the lattice satisfying $\log w \in \mathrm {BMO}$ with suitable estimates of the norms. BMO-regularity was studied extensively, its most elegant equivalent definition for couples of lattices is the existence of majorants $(u, v)$ for arbitrary functions in $(X, Y)$ satisfying $\log u/v \in \mathrm {BMO}$ with suitable control on the norms.
A few years ago, the stability of the real interpolation and the K-closedness of Hardy-type spaces were similarly characterized in terms of a weaker BMO-regularity property, namely that a real interpolation space $(\mathrm L_1, X’ Y)_{\theta, p}$ is BMO-regular. We will explore several alternative characterizations of this property that elucidate its relation to the usual BMO-regularity.
