2022/12/14 by Michael Ruzhansky, Ruzhansky, Michael, Anjali Shriwastawa +3
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2212.07236
openalex publication_date 2022/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case p=1 and 1 ≤ q <∞. This result complements the Hardy inequalities obtained in \citeRV in the case 1< p≤ q<∞. The case p=1 requires a different argument and does not follow as the limit of known inequalities for p>1. As a byproduct, we also obtain the best constant in the established inequality. We give examples obtaining new weighted Hardy inequalities on homogeneous Lie groups, on hyperbolic spaces and on Cartan-Hadamard manifolds for the case p=1 and 1≤ q<∞.