Some remarks on L1 embeddings in the subelliptic setting

被引：2
|
作者：
Krantz, Steven G. [1 ]
Peloso, Marco M. [2 ]
Spector, Daniel [3 ,4 ]
机构：
[1] Washington Univ, Dept Math, St Louis, MO 63130 USA
[2] Univ Milan, Dipartimento Matemat F Enriques, Via C Saldini 50, I-20133 Milan, Italy
[3] Okinawa Inst Sci & Technol Grad Univ, Nonlinear Anal Unit, 1919-1 Tancha, Onna Son, Okinawa, Japan
[4] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu, Taiwan
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2021年 / 202卷
关键词：
Sobolev embeddings; Lorentz spaces; L-1; regime; Stratified group; Subelliptic estimates; LIE-GROUPS; SPACES; OPERATORS; COMPLEX;
D O I：
10.1016/j.na.2020.112149
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we establish an optimal Lorentz estimate for the Riesz potential in the L1 regime in the setting of a stratified group G: Let Q >= 2 be the homogeneous dimension of G and Ia denote the Riesz potential of order a on G. Then, for every alpha is an element of (0, Q), there exists a constant C = C(alpha, Q) > 0 such that parallel to I(alpha)f parallel to L-Q/(Q-alpha),L-1(G) <= C parallel to XI(1)f parallel to(L1(G)) (0.1) for all f is an element of C-c(infinity) (G) such that XI(1)f is an element of L-1(G), where X denotes the horizontal gradient. (C) 2020 TheAuthor(s). Published by Elsevier Ltd.
引用
收藏
页数：11
相关论文
共 50 条
12345