Upper bound of the best constant of a trudinger-moser inequality and its application to A Gagliardo-Nirenberg inequality

Hideo Kozono, Tokushi Sato, Hidemitsu Wadade

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

We will consider a Trudinger-Moser inequality for the critical Sobolev space Hn/p,p(ℝn) with the fractional derivatives in ℝn and obtain an upper bound of the best constant of such an inequality. Moreover, by changing normalization from the homogeneous norm to the inhomogeneous one, we will give the best constant in the Hubert space H n/2,2(ℝn). As an application, we will obtain some lower bound of the best constant of a Gagliardo-Nirenberg inequality. Indiana University Mathematics Journal

Original languageEnglish
Pages (from-to)1951-1974
Number of pages24
JournalIndiana University Mathematics Journal
Volume55
Issue number6
DOIs
Publication statusPublished - 2006
Externally publishedYes

Fingerprint

Trudinger-Moser Inequality
Gagliardo-Nirenberg Inequalities
Best Constants
Upper bound
Hubert Space
Fractional Derivative
Sobolev Spaces
Normalization
Lower bound
Norm

Keywords

  • Average function
  • Fractional integral
  • Gagliadro-Nirenberg inequality
  • Rearrangement
  • Riesz potential
  • Sobolev inequality
  • Trudinger-Moser inequality

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Upper bound of the best constant of a trudinger-moser inequality and its application to A Gagliardo-Nirenberg inequality. / Kozono, Hideo; Sato, Tokushi; Wadade, Hidemitsu.

In: Indiana University Mathematics Journal, Vol. 55, No. 6, 2006, p. 1951-1974.

Research output: Contribution to journalArticle

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