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Rearrangement Invariant Optimal Domain for Monotone Kernel Operators

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Vector Measures, Integration and Related Topics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 201))

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Abstract

For a kernel operator T with values in a Banach function space X, we give monotonicity conditions on the kernel which allow us to describe the rearrangement invariant optimal domain for T (still with values in X). We also study the relation between this optimal domain and the space of integrable functions with respect to the X-valued measure canonically associated to T.

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Author information

Authors and Affiliations

  1. Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, E-46071, Valencia, Spain

    Olvido Delgado

Authors
  1. Olvido Delgado
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Editor information

Editors and Affiliations

  1. Facultad de Matemáticas, Universidad de Sevilla, 41080, Sevilla, Spain

    Guillermo P. Curbera

  2. Fachbereich 6: Mathematik, Universität Siegen, 57068, Siegen, Germany

    Gerd Mockenhaupt

  3. Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt-Ingolstadt, 85072, Eichstätt, Germany

    Werner J. Ricker

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Delgado, O. (2009). Rearrangement Invariant Optimal Domain for Monotone Kernel Operators. In: Curbera, G.P., Mockenhaupt, G., Ricker, W.J. (eds) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol 201. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0211-2_14

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