Abstract
The main aim of this note is to prove sharp weighted integral Hardy inequality and conjugate integral Hardy inequality on homogeneous Lie groups with any quasi-norm for the range \(1<p\le q<\infty \). We also calculate the precise value of sharp constants in respective inequalities, improving the result of Ruzhansky and Verma (Proc R Soc A 475:20180310, 2019) in the case of homogeneous groups.
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Acknowledgements
The second author expresses her sincere gratitude to Ghent analysis and PDE center, Ghent University, Belgium for their financial assistance and hospitality during her research visit.
Funding
MR is supported by the FWO Odysseus 1 Grant G.0H94.18N: Analysis and Partial Differential Equations, the Methusalem Programme of the Grant University Special Research Fund (BOF) (Grant No. 01M01021) and by EPSRC Grant EP/R003025/2. AS is supported by UGC Non-Net Fellowship by Banaras Hindu University, India. The research visit of AS is supported by the Methusalem Programme of the Ghent University Special Research Fund (BOF) Grant No. 01M01021.
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Ruzhansky, M., Shriwastawa, A. & Tiwari, B. A Note on Best Constants for Weighted Integral Hardy Inequalities on Homogeneous Groups. Results Math 79, 29 (2024). https://doi.org/10.1007/s00025-023-02058-3
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DOI: https://doi.org/10.1007/s00025-023-02058-3