Interpolation of quasicontinuous functions
Volume 95 / 2011
Banach Center Publications 95 (2011), 281-286
MSC: Primary 46E30; Secondary 46B70, 46M35, 28A12.
DOI: 10.4064/bc95-0-15
Abstract
If $C$ is a capacity on a measurable space, we prove that the restriction of the $K$-functional $K(t,f;L^p(C), L^\infty(C))$ to quasicontinuous functions $f\in QC$ is equivalent to \[ K(t,f;L^p(C) \cap QC, L^\infty(C)\cap QC). \] We apply this result to identify the interpolation space $(L^{p_0,q_0}(C) \cap QC, L^{p_1,q_1}(C) \cap QC)_{\theta, q}$.
