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 / 202期

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

页数：11

共 22 条

[1] Besov and Triebel-Lizorkin spaces on Lie groups [J].

Bruno, Tommaso ;

Peloso, Marco M. ;

Vallarino, Maria .

MATHEMATISCHE ANNALEN, 2020, 377 (1-2) :335-377

[2] Sobolev spaces on Lie groups: Embedding theorems and algebra properties [J].

Bruno, Tommaso ;

Peloso, Marco M. ;

Tabacco, Anita ;

Vallarino, Maria .

JOURNAL OF FUNCTIONAL ANALYSIS, 2019, 276 (10) :3014-3050

[3]

Chanillo S, 2009, MATH RES LETT, V16, P487, DOI 10.4310/MRL.2009.v16.n3.a9

[4] Sobolev algebras on Lie groups and Riemannian manifolds [J].

Coulhon, T ;

Russ, E ;

Tardivel-Nachef, V .

AMERICAN JOURNAL OF MATHEMATICS, 2001, 123 (02) :283-342

[5] WEAK TYPE (1, 1) ESTIMATES FOR HEAT KERNEL MAXIMAL FUNCTIONS ON LIE-GROUPS [J].

COWLING, M ;

GAUDRY, G ;

GIULINI, S ;

MAUCERI, G .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 323 (02) :637-649

[6]

FOLLAND GB, 1975, ARK MAT, V13, P161, DOI 10.1007/BF02386204

[7] ESTIMATES FOR DELTA-BAR B COMPLEX AND ANALYSIS ON HEISENBERG GROUP [J].

FOLLAND, GB ;

STEIN, EM .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1974, 27 (04) :429-522

[8]

Garofalo N, 1996, COMMUN PUR APPL MATH, V49, P1081, DOI 10.1002/(SICI)1097-0312(199610)49:10<1081::AID-CPA3>3.0.CO

[9]

2-A

[10]

Grafakos L, 2014, GRAD TEXTS MATH, V250, DOI 10.1007/978-1-4939-1230-8

← 1 2 3 →