A class of weighted Hardy type inequalities in RN

被引:0
作者
Canale, Anna [1 ]
机构
[1] Univ Salerno, Dipartimento Ingn Informaz Elettr & Matemat Appli, Via Giovanni Paolo II,132, I-84084 Salerno, Italy
关键词
Weighted Hardy type inequalities; Kolmogorov operators; Singular potentials; Evolution problems; OPERATORS; SPACES; UNIQUENESS; BOUNDS;
D O I
10.1007/s11587-021-00628-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In the paper we prove the weighted Hardy type inequality 1 integral V-RN phi(2)mu(x)dx <= integral(RN) vertical bar del phi vertical bar(2)mu(x)dx + K integral(RN)phi(2)mu(x)dx, (1) for functions. in a weighted Sobolev space H-mu(1), for a wider class of potentials V than inverse square potentials and for weight functions mu of a quite general type. The case mu = 1 is included. To get the result we introduce a generalized vector field method. The estimates apply to evolution problems with Kolmogorov operators Lu = Delta u + del mu/mu center dot del u perturbed by singular potentials.
引用
收藏
页码:619 / 631
页数:13
相关论文
共 50 条
[41]   Weighted inequalities for commutators of potential type operators [J].
Li, Wenming .
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2007, 44 (06) :1233-1241
[42]   Quantitative Weighted Mixed Weak-Type Inequalities for Classical Operators [J].
Ombrosi, Sheldy ;
Perez, Carlos ;
Recchi, Jorgelina .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2016, 65 (02) :615-640
[43]   MULTI-DIMENSIONAL HARDY TYPE INEQUALITIES IN HOLDER SPACES [J].
Burtseva, Evgeniya ;
Lundberg, Staffan ;
Persson, Lars-Erik ;
Samko, Natasiia .
JOURNAL OF MATHEMATICAL INEQUALITIES, 2018, 12 (03) :719-729
[44]   Best constants in bipolar Lp Hardy-type inequalities [J].
Cazacu, Cristian ;
Rugina, Teodor .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 530 (01)
[45]   SOME NEW REFINED HARDY-TYPE INEQUALITIES WITH KERNELS [J].
Cizmesija, Aleksandra ;
Krulic, Kristina ;
Pecaric, Josip .
JOURNAL OF MATHEMATICAL INEQUALITIES, 2010, 4 (04) :481-503
[46]   SOME NEW ITERATED HARDY-TYPE INEQUALITIES AND APPLICATIONS [J].
Bernardis, A. L. ;
Ortega Salvador, Pedro .
JOURNAL OF MATHEMATICAL INEQUALITIES, 2017, 11 (02) :577-594
[47]   A Bakry-Emery criterion for weighted contractivity and L2-Hardy inequalities [J].
Qiu, Yaozhong .
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2025, 27 (04)
[48]   NEW WEIGHTED HARDY-TYPE INEQUALITIESFOR MONOTONE FUNCTIONS [J].
Kalybay, Aigerim Aisultankyzy ;
Temirkhanova, Ainur Maralkyzy .
EURASIAN MATHEMATICAL JOURNAL, 2024, 15 (04) :54-65
[49]   THE FRACTIONAL TYPE MARCINKIEWICZ INTEGRALS AND COMMUTATORS ON WEIGHTED HARDY SPACES [J].
Han, Yanyan ;
Wu, Huoxiong .
ACTA MATHEMATICA SCIENTIA, 2023, 43 (05) :1981-1996
[50]   On some hyperbolic type equations and weighted anisotropic Hardy operators [J].
Lundberg, Staffan ;
Samko, Natasha .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (05) :1414-1421