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Mathematics > Classical Analysis and ODEs

arXiv:2212.07236 (math)
[Submitted on 14 Dec 2022]

Title:Hardy inequalities on metric measure spaces, IV: The case $p=1$

Authors:Michael Ruzhansky, Anjali Shriwastawa, Bankteshwar Tiwari
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Abstract:In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case $p=1$ and $1 \leq q <\infty.$ This result complements the Hardy inequalities obtained in \cite{RV} in the case $1< p\le q<\infty.$ 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 $1\le q<\infty.$
Comments: 11 pages, comments and suggestions are welcome
Subjects: Classical Analysis and ODEs (math.CA)
Cite as: arXiv:2212.07236 [math.CA]
  (or arXiv:2212.07236v1 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.2212.07236

Submission history

From: Anjali Shriwastawa [view email]
[v1] Wed, 14 Dec 2022 14:17:07 UTC (12 KB)
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