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On Gagliardo-Nirenberg Type Inequalities
Karlstad University, Faculty of Technology and Science, Department of Mathematics.ORCID iD: 0000-0001-5459-0796
Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain..
2014 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 20, no 3, 577-607 p.Article in journal (Refereed) PublishedText
Abstract [en]

We present a Gagliardo-Nirenberg inequality which bounds Lorentz norms of a function by Sobolev norms and homogeneous Besov quasinorms with negative smoothness. We prove also other versions involving Besov or Triebel-Lizorkin quasinorms. These inequalities can be considered as refinements of Sobolev type embeddings. They can also be applied to obtain Gagliardo-Nirenberg inequalities in some limiting cases. Our methods are based on estimates of rearrangements in terms of heat kernels. These methods enable us to cover also the case of Sobolev norms with p = 1.

Place, publisher, year, edition, pages
Springer, 2014. Vol. 20, no 3, 577-607 p.
Keyword [en]
Gagliardo-Nirenberg inequality, Sobolev spaces, Besov spaces, Triebel-Lizorkin spaces
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-41523DOI: 10.1007/s00041-014-9320-yISI: 000337789300007OAI: oai:DiVA.org:kau-41523DiVA: diva2:923136
Available from: 2016-04-25 Created: 2016-04-11 Last updated: 2016-06-12Bibliographically approved

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Kolyada, Viktor
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