A note on best constants for Weighted Integral Hardy inequalities on homogeneous groups

Michael Ruzhansky; Anjali Shriwastawa; Bankteshwar Tiwari

A note on best constants for Weighted Integral Hardy inequalities on homogeneous groups

Analysis of PDEs 2022-02-15 v1

Authors: Michael Ruzhansky , Anjali Shriwastawa , Bankteshwar Tiwari

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 $1<p\leq q<\infty.$ We also calculate the precise value of sharp constants in respective inequalities, improving the result of $[19]$ in the case of homogeneous groups.

Keywords

weighted integral hardy inequality conjugate integral hardy inequality homogeneous lie groups quasi-norm sharp constants

Cite

@article{arxiv.2202.05873,
  title  = {A note on best constants for Weighted Integral Hardy inequalities on homogeneous groups},
  author = {Michael Ruzhansky and Anjali Shriwastawa and Bankteshwar Tiwari},
  journal= {arXiv preprint arXiv:2202.05873},
  year   = {2022}
}

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11 pages

A note on best constants for Weighted Integral Hardy inequalities on homogeneous groups

Abstract

Keywords

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