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Real interpolation with weighted rearrangement invariant Banach function spaces

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Abstract

Motivated by recent applications of weighted norm inequalities to maximal regularity of first- and second-order Cauchy problems, we study real interpolation spaces on the basis of general Banach function spaces and, in particular, weighted rearrangement invariant Banach function spaces. We show equivalence of the trace method and the K-method, identify real interpolation spaces between a Banach space and the domain of a sectorial operator, and reprove an extension of Dore’s theorem on the boundedness of \(H^\infty \)-functional calculus to this general setting.

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Authors and Affiliations

  1. Institut für Analysis Fachrichtung Mathematik, TU Dresden, 01062, Dresden, Germany

    Ralph Chill & Sebastian Król

  2. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland

    Sebastian Król

Authors
  1. Ralph Chill
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  2. Sebastian Król
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Correspondence to Ralph Chill.

Additional information

The second author was partially supported by the Alexander von Humboldt Foundation and Narodowe Centrum Nauki Grant DEC-2011/03/B/ST1/00407 and DEC-2014/13/B/ST1/03153.

Dedicated to Jan Prüss in great admiration.

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Chill, R., Król, S. Real interpolation with weighted rearrangement invariant Banach function spaces. J. Evol. Equ. 17, 173–195 (2017). https://doi.org/10.1007/s00028-016-0366-y

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