Geodesic
Interpolation of a regular subspace complementing the span of a radially singular function
Konstantin Zerulla 1
1 Department of Mathematics Karlsruhe Institute of Technology Englerstr. 2 76131 Karlsruhe, Germany
Studia Mathematica, Tome 265 (2022) no. 2, pp. 197-210 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm210621-12-8
Keywords: analyze interpolation sum subspace consisting regular functions span function alpha type singularity particular determine interpolation parameters which interpolation space subspace regular functions still closed subspace main tool here result ivanov kalton interpolation subspaces apply study k functional alpha singular function turns out k functional possesses upper lower bounds have common decay rate zero

Konstantin Zerulla  1

1 Department of Mathematics Karlsruhe Institute of Technology Englerstr. 2 76131 Karlsruhe, Germany 
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Konstantin Zerulla. Interpolation of a regular subspace complementing the span of a radially singular function. Studia Mathematica, Tome 265 (2022) no. 2, pp. 197-210. doi: 10.4064/sm210621-12-8

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