Endpoint L1 estimates for Hodge systems

被引：0

作者：

Hernandez, Felipe ^{[1
]}

Raita, Bogdan ^{[2
,3
]}

Spector, Daniel ^{[4
,5
]}

机构：

[1] Stanford Univ, Dept Math, Bldg 380, Stanford, CA 94305 USA

[2] Scuola Normale Super Pisa, Ennio De Giorgi Math Res Ctr, Piazza Cavalieri 7, I-56126 Pisa, Italy

[3] Alexandru Ioan Cuza Univ, Dept Math, Blvd Carol I 11, Iasi 700506, Romania

[4] Natl Taiwan Normal Univ, Dept Math, 88,Sect 4,Tingzhou Rd, Taipei 116, Taiwan

[5] Okinawa Inst Sci & Technol Grad Univ, Nonlinear Anal Unit, 1919-1 Tancha, Kunigami, Okinawa, Japan

来源：

MATHEMATISCHE ANNALEN | 2023年 / 385卷 / 3-4期

关键词：

VECTOR-FIELDS; DIV-CURL; EMBEDDINGS; OPERATORS; SPACES;

D O I：

10.1007/s00208-022-02383-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let d >= 2. In this paper we give a simple proof of the endpoint Besov-Lorentz estimate parallel to I alpha F parallel to B-d/(d-alpha),1(0,1) (R-d;R-k) <= C parallel to F parallel to(L)1(R-d;R-k) for all F is an element of L-1 (R-d ; R-k) which satisfy a first order cocancelling differential constraint, where alpha is an element of (0, d) and I-alpha is a Riesz potential. We show how this implies endpoint Besov-Lorentz estimates for Hodge systems with L-1 data via fractional integration for exterior derivatives.

引用

页码：1923 / 1946

页数：24

共 32 条

[1] Adams DR., 1996, Function spaces and potential theory, DOI [10.1007/978-3-662-03282-4, DOI 10.1007/978-3-662-03282-4]
[2] Alvino A., 1977, Boll. Un. Mat. Ital., V14, P148
[3] Sobolev martingales
Ayoush, Rami
Stolyarov, Dmitriy
Wojciechowski, Michal
[J]. REVISTA MATEMATICA IBEROAMERICANA, 2021, 37 (04) : 1225 - 1246
[4] Bourgain J, 2004, PUBL MATH-PARIS, P1, DOI 10.1007/s10240-004-0019-5
[5] New estimates for the Laplacian, the div-curl, and related Hodge systems
Bourgain, J
Brezis, H
[J]. COMPTES RENDUS MATHEMATIQUE, 2004, 338 (07) : 539 - 543
[6] Bourgain J, 2007, J EUR MATH SOC, V9, P277
[7] Federer H., 1969, GRUNDLEHREN MATH WIS, V153
[8] Grafakos L., 2008, CLASSICAL FOURIER AN, DOI DOI 10.1007/978-1-4939-1194-3
[9] Guerra A., ARXIV190903923
[10] Hernandez F., ARXIV200805639

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