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A Generalized Hardy Operator on Rearrangement Invariant Spaces

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Current Trends in Analysis, its Applications and Computation

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

In this paper we consider a weighted generalization of the Hardy operator acting on a rearrangement invariant function space. We give necessary and sufficient conditions for this linear operator to be bounded on a rearrangement invariant function space in terms of its upper Boyd index and the integrability of the norm of the dilation operator with respect to the considered weight.

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References

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Acknowledgements

We would like to thank the referee for his/her comments which helped us to improve the paper.

The first author is supported by Ministerio de Ciencia, Innovación y Universidades Project PGC2018-095366-B-I00 and the second author is supported by CONACYT, grant 711238.

Author information

Authors and Affiliations

  1. Universidad de Valencia, Valencia, Spain

    Oscar Blasco

  2. Universidad de Sonora, Departamento de Matemáticas, Hermosillo, Mexico

    Carolina Espinoza-Villalva

Authors
  1. Oscar Blasco
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  2. Carolina Espinoza-Villalva
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Corresponding author

Correspondence to Oscar Blasco .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Paula Cerejeiras

  2. Institut of Applied Analysis, TU Bergakademie Freiberg, Freiberg, Germany

    Michael Reissig

  3. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Irene Sabadini

  4. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

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Blasco, O., Espinoza-Villalva, C. (2022). A Generalized Hardy Operator on Rearrangement Invariant Spaces. In: Cerejeiras, P., Reissig, M., Sabadini, I., Toft, J. (eds) Current Trends in Analysis, its Applications and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-87502-2_32

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