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Limiting reiteration for real interpolation with logarithmic functions

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Abstract

The real interpolation method \( {\overline{X}}_{\theta ,q,b}=(X_0,X_1)_{\theta ,q,b} \) involving iterated logarithms with any number of iterations is considered. Reiteration relations of the types \( (X_0,{\overline{X}}_{0,q,a})_{\theta ,r,b} \) and \( ({\overline{X}}_{1,q,a}X_1)_{\theta ,r,b} \) \( (0\le \theta \le 1)\) are investigated. Using any number of iterations allows in particular obtaining effects where the resulting space includes three iterated logarithms although the initial scale includes only the uniterated logarithm. Application to Lorentz–Zygmund spaces is given.

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  1. Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB, Gutleuthausstr. 1, 76275, Ettlingen, Germany

    Leo R. Ya. Doktorski

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  1. Leo R. Ya. Doktorski
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Correspondence to Leo R. Ya. Doktorski.

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To my friend Sergei Grudsky on the occasion of his 60th birthday.

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Doktorski, L.R.Y. Limiting reiteration for real interpolation with logarithmic functions. Bol. Soc. Mat. Mex. 22, 679–693 (2016). https://doi.org/10.1007/s40590-016-0116-8

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  • DOI: https://doi.org/10.1007/s40590-016-0116-8

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