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Function Spaces and Inequalities pp 117–135Cite as

Gagliardo-Nirenberg Inequalities for Spaces with Dominating Mixed Derivatives

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 206))

Abstract

We study inequalities of Gagliardo-Nirenberg type for scales of function spaces with dominating mixed smoothness. This situation is more sophisticated than in the classical isotropic case. We show that satisfying results can be obtained using the concept of refined dominating mixed smoothness both in the case of Triebel-Lizorkin and Besov-type spaces.

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Authors and Affiliations

  1. Institute of Mathematics, Friedrich Schiller University Jena, 07737, Jena, Germany

    Dorothee D. Haroske & Hans-Jürgen Schmeisser

Authors
  1. Dorothee D. Haroske
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  2. Hans-Jürgen Schmeisser
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Correspondence to Dorothee D. Haroske .

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Editors and Affiliations

  1. Department of Mathematics, South Asian University, New Delhi, Delhi, India

    Pankaj Jain

  2. Faculty of Mathematics & Computer Science, Friedrich Schiller University Jena, Jena, Thüringen, Germany

    Hans-Jürgen Schmeisser

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Haroske, D.D., Schmeisser, HJ. (2017). Gagliardo-Nirenberg Inequalities for Spaces with Dominating Mixed Derivatives. In: Jain, P., Schmeisser, HJ. (eds) Function Spaces and Inequalities. Springer Proceedings in Mathematics & Statistics, vol 206. Springer, Singapore. https://doi.org/10.1007/978-981-10-6119-6_5

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