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

Michael Ruzhansky; Anjali Shriwastawa; Bankteshwar Tiwari

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

Classical Analysis and ODEs 2022-12-15 v1

Authors: Michael Ruzhansky , Anjali Shriwastawa , Bankteshwar Tiwari

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 $1\le q<\infty.$

Keywords

Hardy inequalities metric measure spaces polar decompositions two-weight best constant homogeneous Lie groups

Cite

@article{arxiv.2212.07236,
  title  = {Hardy inequalities on metric measure spaces, IV: The case $p=1$},
  author = {Michael Ruzhansky and Anjali Shriwastawa and Bankteshwar Tiwari},
  journal= {arXiv preprint arXiv:2212.07236},
  year   = {2022}
}

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

Abstract

Keywords

Cite

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