FACTORIZATIONS AND UNIFIED HARDY INEQUALITIES ON HOMOGENEOUS LIE GROUPS
https://doi.org/10.55452/1998-6688-2024-21-3-147-157
Abstract
In this note we obtain Hardy and critical Hardy inequalities with any homogeneous quasi-norm in unified way. Actually, we show a sharp remainder formula for these results. In particular, our identity implies corresponding Hardy and critical Hardy inequalities with any homogeneous quasi-norm for the radial derivative operator, thus yielding improved versions of corresponding classical counterparts. Moreover, we discuss extensions of these results in the setting of Folland and Stein’s homogeneous Lie groups. Such a more general setting is convenient for the distillation of those results of harmonic analysis depending only on the group and dilation structures, which is one of our motivations working in the setting. Our approach based on the factorization method of differential operators introduced by Gesztesy and Littlejohn. As an application, we show Caffarelli-Kohn-Nirenberg type inequalities with more general weight. Because of the freedom in the choice of any homogeneous quasi-norm, our results give new insights already in both anisotropic ℝn and isotropic ℝn .
Supporting agencies: This research is funded by the Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant No. AP14871691).
About the Authors
K. Apseit
SDU University;
Institute of Mathematics and Mathematical Modeling
Kazakhstan
Kazakhstan
Master
040900, Kaskelen;
050010, Almaty
N. Yessirkegenov
KIMEP University
Kazakhstan
Kazakhstan
PhD
050010, Almaty
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Review
For citations:
Apseit K., Yessirkegenov N. FACTORIZATIONS AND UNIFIED HARDY INEQUALITIES ON HOMOGENEOUS LIE GROUPS. Herald of the Kazakh-British technical university. 2024;21(3):147-157. https://doi.org/10.55452/1998-6688-2024-21-3-147-157
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