Euler semigroup, Hardy–Sobolev and Gagliardo–Nirenberg type inequalities on homogeneous groups
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Date
2020-06-10
Authors
Ruzhansky, Michael
Suragan, Durvudkhan
Yessirkegenov, Nurgissa
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
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.
Description
Keywords
Hardy inequality, Sobolev inequality, Euler semigroup, Homogeneous group, Research Subject Categories::MATHEMATICS
Citation
Ruzhansky, M., Suragan, D., & Yessirkegenov, N. (2020). Euler semigroup, Hardy–Sobolev and Gagliardo–Nirenberg type inequalities on homogeneous groups. Semigroup Forum, 101(1), 162–191. https://doi.org/10.1007/s00233-020-10110-9