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A Bump Theorem for Weighted Embeddings and Maximal Operator: The Bellman Function Approach

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Harmonic Analysis, Partial Differential Equations, Banach Spaces, and Operator Theory (Volume 2)

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 5))

Abstract

We give here an “automatic” proof of a weighted embedding theorem with a bumping of the weight. It implies a well-known weighted theorem of C. Pérez.

To Cora Sadosky with Gratitude for Her Friendship and Encouragements

AV is partially supported by the NSF grant DMS-1265549 and by the Hausdorff Institute for Mathematics, Bonn, Germany

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Acknowledgements

The author is grateful to F. Nazarov and A. Reznikov for the important discussions and valuable advices. The author also thanks the referee for many suggestions that improved the exposition.

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Alexander Volberg

Authors
  1. Alexander Volberg
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Correspondence to Alexander Volberg .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico, USA

    María Cristina Pereyra

  2. Department of Mathematics, Venezuelan Institute for Scientific Research, Caracas, Venezuela

    Stefania Marcantognini

  3. Department of Mathematical Sciences, Georgia Southern University, Statesboro, Georgia, USA

    Alexander M. Stokolos

  4. Department of Mathematical and Actuarial Sciences, Roosevelt University Chicago, Chicago, Illinois, USA

    Wilfredo Urbina

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Volberg, A. (2017). A Bump Theorem for Weighted Embeddings and Maximal Operator: The Bellman Function Approach. In: Pereyra, M., Marcantognini, S., Stokolos, A., Urbina, W. (eds) Harmonic Analysis, Partial Differential Equations, Banach Spaces, and Operator Theory (Volume 2). Association for Women in Mathematics Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-51593-9_16

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