Interpolation inequalities in function spaces of Sobolev-Lorentz type

Autor:	Byeon, Jaeseong, Kim, Hyunseok, Oh, Jisu
Rok vydání:	2021
Předmět:	Mathematics - Functional Analysis Mathematics - Analysis of PDEs 46E35 (Primary) 42B35 35A23 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Interpolation inequalities in Triebel-Lizorkin-Lorentz spaces and Besov-Lorentz spaces are studied for both inhomogeneous and homogeneous cases. First we establish interpolation inequalities under quite general assumptions on the parameters of the function spaces. Several results on necessary conditions are also provided. Next, utilizing the interpolation inequalities together with some embedding results, we prove Gagliardo-Nirenberg inequalities for fractional derivatives in Lorentz spaces, which do hold even for the limiting case when one of the parameters is equal to 1 or $\infty$. Comment: 47 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.07518 Zobrazit plný text záznamu View this record from Arxiv