@inproceedings{58c17fd185e74e17914eb058671f050e,

title = "A Survey of Hardy Type Inequalities on Homogeneous Groups",

abstract = "In this review paper, we survey Hardy type inequalities from the point of view of Folland and Stein{\textquoteright}s homogeneous groups. Particular attention is paid to Hardy type inequalities on stratified groups which give a special class of homogeneous groups. In this environment, the theory of Hardy type inequalities becomes intricately intertwined with the properties of sub-Laplacians and more general subelliptic partial differential equations. Particularly, we discuss the Badiale-Tarantello conjecture and a conjecture on the geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant.",

keywords = "Hardy inequality, Heisenberg group, Homogeneous group, Nilpotent Lie group, Stratified group, Sub-Laplacian",

author = "Durvudkhan Suragan",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 12th International Society for Analysis, its Applications and Computation, ISAAC 2019 ; Conference date: 29-07-2019 Through 02-08-2019",

year = "2022",

doi = "10.1007/978-3-030-97127-4_4",

language = "English",

isbn = "9783030971267",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "99--122",

editor = "Paula Cerejeiras and Michael Reissig",

booktitle = "Mathematical Analysis, its Applications and Computation - ISAAC 2019",

}