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Interpolation of uniformly absolutely continuous operators

Authors

  • Fernando Cobos,

    1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain. Phone: +34 913 944 453, Fax: +34 913 944 613
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  • Amiran Gogatishvili,

    1. Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic. Phone: +420 222 090 786, Fax: +420 222 090 701
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  • Bohumír Opic,

    1. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic. Phone: +420 221 913 367, Fax: +420 222 323 390
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  • Luboš Pick

    Corresponding author
    1. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic. Phone: +420 221 913 367, Fax: +420 222 323 390
    • Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic. Phone: +420 221 913 264, Fax: +420 222 323 390
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  • This paper is dedicated to Professor Hans Triebel on the occasion of his 75th birthday

Abstract

We develop a method suitable for interpolation of uniformly absolutely continuous operators. We then apply this method to establishing compactness of operators and embeddings especially in the limiting situations, where the classical interpolation methods fail. We study types of certain interpolation methods and their sharpness.

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