Interpolation of a regular subspace complementing the span of a radially singular function
Volume 265 / 2022
Studia Mathematica 265 (2022), 197-210
MSC: 46B70, 26A30, 46E35.
DOI: 10.4064/sm210621-12-8
Published online: 7 March 2022
Abstract
We analyze the interpolation of the sum of a subspace, consisting of regular functions, with the span of a function with $r^{\alpha }$-type singularity. In particular, we determine all interpolation parameters, for which the interpolation space of the subspace of regular functions is still a closed subspace. The main tool is here a result by Ivanov and Kalton on interpolation of subspaces. To apply it, we study the $K$-functional of the $r^{\alpha }$-singular function. It turns out that the $K$-functional possesses upper and lower bounds that have a common decay rate at zero.
