@article{da2dd0d4b416463880e20bedf22ef9ae,
title = "Euler semigroup, Hardy–Sobolev and Gagliardo–Nirenberg type inequalities on homogeneous groups",
abstract = "In this paper we describe the Euler semigroup {e-tE∗E}t>0 on homogeneous Lie groups, which allows us to obtain various types of the Hardy–Sobolev and Gagliardo–Nirenberg type inequalities for the Euler operator E. Moreover, the sharp remainder terms of the Sobolev type inequality, maximal Hardy inequality and | · | -radial weighted Hardy–Sobolev type inequality are established.",
keywords = "Euler semigroup, Hardy inequality, Homogeneous group, Sobolev inequality",
author = "Michael Ruzhansky and Durvudkhan Suragan and Nurgissa Yessirkegenov",
note = "Funding Information: The first author was supported in parts by the FWO Odysseus 1 Grant G.0H94.18N: Analysis and Partial Differential Equations, the EPSRC Grant EP/R003025/1 and by the Leverhulme Grant RPG-2017-151. The second author was supported by the Nazarbayev University program 091019CRP2120 and the Nazarbayev University Grant 240919FD3901. The third author was supported by the FWO Odysseus 1 Grant G.0H94.18N: Analysis and Partial Differential Equations, by the LMS Early Career Fellowship Grant ECF-1819-12 and by the MESRK Grant AP05133271. Publisher Copyright: {\textcopyright} 2020, The Author(s).",
year = "2020",
doi = "10.1007/s00233-020-10110-9",
language = "English",
volume = "101",
pages = "162--191",
journal = "Semigroup Forum",
issn = "0037-1912",
publisher = "Springer New York",
number = "1",
}