Generalized Gagliardo–Nirenberg inequalities using Lorentz spaces, BMO, Hölder spaces and fractional Sobolev spaces. (August 2018)

• Record Type: Journal Article
• Authors: Dao, Nguyen Anh; Díaz, Jesus Ildefonso; Nguyen, Quoc-Hung
• Is Part Of: Nonlinear analysis. Volume 173(2018)
• Page Start: 146
• Page End: 153
• Publication Date: 2018-08
• Subjects: Gagliardo–Nirenberg's inequality -- Lorentz spaces -- BMO -- Lipschitz space -- Fractional Sobolev space; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.04.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The main purpose of this paper is to prove some generalized Gagliardo–Nirenberg interpolation inequalities involving the Lorentz spaces L p, α, BMO and the fractional Sobolev spaces W s, p, including also C ̇ η Hölder spaces. Although some of the results can be alternatively obtained by using interpolation spaces (specifically, the reiteration theorem), the precise form of the inequalities stated here appears to be novel and, moreover, the proofs given in the present paper are self-contained (save for the use of the John–Nirenberg inequality for the BMO result) in contrast to the other mentioned approach. The use of C ̇ η Hölder spaces in such Gagliardo–Nirenberg inequalities seems to be new in the literature.