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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Interpolation of a regular subspace complementing the span of a radially singular function

### Tom 265 / 2022

Studia Mathematica 265 (2022), 197-210 MSC: 46B70, 26A30, 46E35. DOI: 10.4064/sm210621-12-8 Opublikowany online: 7 March 2022

#### Streszczenie

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.