Improved Hardy and Hardy-Rellich type inequalities with Bessel pairs via factorizations

被引：15

作者：

Nguyen Tuan Duy ^{[1
]}

Nguyen Lam ^{[2
]}

Nguyen Anh Triet ^{[3
]}

机构：

[1] Univ Finance Mkt, Fac Econ & Law, 2-4 Tran Xuan Soan St, Ho Chi Minh City, Vietnam

[2] Mem Univ Newfoundland, Sch Sci & Environm, Grenfell Campus, Corner Book, NF A2H5G4, Canada

[3] Duy Tan Univ, Inst Fundamental & Appl Sci, 3 Quang Trung, Danang City, Vietnam

来源：

JOURNAL OF SPECTRAL THEORY | 2020年 / 10卷 / 04期

关键词：

Hardy inequality; Hardy-Rellich inequality; factorizations of differential operators; UNIFIED APPROACH; REMAINDER; CONSTANTS;

D O I：

10.4171/JST/327

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using the factorizations of suitable operators, we establish several identities that give simple and direct understandings as well as provide the remainders and "virtual" optimizers of several the Hardy and Hardy-Rellich type inequalities.

引用

页码：1277 / 1302

页数：26

共 37 条

[1] An improved Hardy-Sobolev inequality and its application
Adimurthi
Chaudhuri, N
Ramaswamy, M
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (02) : 489 - 505
[2] Alexander A, 2015, ANAL GEOMETRY HARDYS
[3] [Anonymous], 1999, The Maz'ya Anniversary Collection, DOI DOI 10.1007/978-3-0348-8672-7_5
[4] A unified approach to improved Lp hardy inequalities with best constants
Barbatis, G
Filippas, S
Tertikas, A
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (06) : 2169 - 2196
[5] Hardy-Rellich inequalities with boundary remainder terms and applications
Berchio, Elvise
Cassani, Daniele
Gazzola, Filippo
[J]. MANUSCRIPTA MATHEMATICA, 2010, 131 (3-4) : 427 - 458
[6] Brezis H., 1997, Rev. Mat. Univ. Complut. Madrid, V10, P443
[7] The Rellich inequality
Edmunds, D. E.
Evans, W. D.
[J]. REVISTA MATEMATICA COMPLUTENSE, 2016, 29 (03): : 511 - 530
[8] Evans W.D., 2007, J MATH INEQUAL, V1, P473
[9] Evans W, 2009, CHANDOS INF PROF SER, P33
[10] Non-linear ground state representations and sharp Hardy inequalities
Frank, Rupert L.
Seiringer, Robert
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (12) : 3407 - 3430

← 1 2 3 4 →