@article{d053975405a94f648ea126e5ca932aa9,
title = "Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups",
abstract = "In this note, we prove the Stein–Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs. Also, we give a simple proof of the Hardy–Littlewood–Sobolev inequality on general homogeneous Lie groups.",
keywords = "22E30, 43A80, fractional integral, fractional operator, Hardy–Littlewood–Sobolev inequality, homogeneous Lie group, Riesz potential, Stein–Weiss inequality",
author = "Aidyn Kassymov and Michael Ruzhansky and Durvudkhan Suragan",
note = "Funding Information: Theauthors weresupportedinpartsby theFWO Odysseus Project, bytheEngineering andPhysical Sciences Research Council (EPSRC) grant EP/R003025/1, by the Leverhulme grant RPG-2017-151, NU SPG as well as by the MESRK grant AP05130981. Funding Information: The authors were supported in parts by the FWO Odysseus Project, by the Engineering and Physical Sciences Research Council (EPSRC) grant EP/R003025/1, by the Leverhulme grant RPG-2017-151, NU SPG as well as by the MESRK grant AP05130981. Publisher Copyright: {\textcopyright} 2019, {\textcopyright} 2019 Informa UK Limited, trading as Taylor & Francis Group.",
year = "2019",
month = jan,
day = "1",
doi = "10.1080/10652469.2019.1597080",
language = "English",
volume = "30",
pages = "643--655",
journal = "Integral Transforms and Special Functions",
issn = "1065-2469",
publisher = "Taylor and Francis",
number = "8",
}