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The boundedness of operators in Muckenhoupt weighted Morrey spaces via extrapolation techniques and duality

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Abstract

The bidual of the closure of smooth functions with respect to the Morrey norm coincides with the Morrey space. This assertion is generalized to some Muckenhoupt weighted Morrey spaces. We combine this fact with basic extrapolation techniques due to Rubio de Francia adapted to weighted Morrey spaces. This leads to new results on the boundedness of operators even for the unweighted case.

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Acknowledgments

We thank Javier Duoandikoetxea (UPV/EHU) for useful hints with respect to Section 5 dealing with extrapolation in Morrey spaces.

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Authors and Affiliations

  1. Departamento de Matemáticas/Matematika Saila, Universidad del País Vasco/Euskal Herriko Unibertsitatea, Apdo. 644, 48080, Bilbao, Spain

    Marcel Rosenthal

  2. Mathematisches Institut, Universität Jena, Ernst-Abbe-Platz 2, 07743, Jena, Germany

    Hans-Jürgen Schmeisser

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  1. Marcel Rosenthal
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  2. Hans-Jürgen Schmeisser
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Correspondence to Marcel Rosenthal.

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The first author is supported by the German Academic Exchange Service (DAAD).

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Rosenthal, M., Schmeisser, HJ. The boundedness of operators in Muckenhoupt weighted Morrey spaces via extrapolation techniques and duality. Rev Mat Complut 29, 623–657 (2016). https://doi.org/10.1007/s13163-016-0208-z

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