On Gagliardo-Nirenberg Type Inequalities

  1. Kolyada, V.I. 2
  2. Pérez Lázaro, F.J. 1
  1. 1 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

  2. 2 Karlstad University

    Karlstad University

    Karlstad, Suecia

    GRID grid.20258.3d

Journal of Fourier Analysis and Applications

ISSN: 1069-5869

Year of publication: 2014

Volume: 20

Issue: 3

Pages: 577-607

Type: Article

Export: RIS
DOI: 10.1007/s00041-014-9320-y SCOPUS: 2-s2.0-84902372706 WoS: 000337789300007 arXiv: 1211.1315v1 GOOGLE SCHOLAR lock_openOpen access editor


Cited by

  • Scopus Cited by: 5 (12-06-2021)

Journal Citation Reports

  • Year 2014
  • Journal Impact Factor: 1.118
  • Best Quartile: Q2
  • Area: MATHEMATICS, APPLIED Quartile: Q2 Rank in area: 76/257 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2014
  • SJR Journal Impact: 1.11
  • Best Quartile: Q1
  • Area: Applied Mathematics Quartile: Q1 Rank in area: 103/574
  • Area: Mathematics (miscellaneous) Quartile: Q1 Rank in area: 76/409
  • Area: Analysis Quartile: Q2 Rank in area: 36/130


  • Year 2014
  • CiteScore of the Journal : 2.0
  • Area: Mathematics (all) Percentile: 84
  • Area: Analysis Percentile: 73
  • Area: Applied Mathematics Percentile: 62


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. © 2014 Springer Science+Business Media New York.