Pith. sign in

REVIEW 3 cited by

$L^{p}$-Caffarelli-Kohn-Nirenberg inequalities and their stabilities

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2310.07083 v1 pith:PSSZNDC3 submitted 2023-10-10 math.AP

Anh Xuan Do , Joshua Flynn , Nguyen Lam , Guozhen Lu This is my paper · ORCID
classification math.AP
keywords caffarelli-kohn-nirenberginequalitieshardytheoremsconstantsestablishidentitiesresults
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We establish a general identity (Theorem 1.2) that implies both the $L^{p}$-Hardy identities and the $L^{p}$-Caffarelli-Kohn-Nirenberg identities (Theorems 1.3 and 1.4) and $L^{p}$-Hardy inequalities and the $L^{p}$-Caffarelli-Kohn-Nirenberg inequalities (Theorems 1.5 and 1.6)). Weighted $L^{p}$-Caffarelli-Kohn-Nirenberg inequalities with nonradial weights are also obtained. (Theorem 1.7). Our results provide simple interpretations to the sharp constants, as well as the existence and non-existence of the optimizers, of several $L^{p}$-Hardy and $L^{p}% $-Caffarelli-Kohn-Nirenberg inequalities. As applications of our main results, we are able to establish stabilities of a class of $L^{2}$ and $L^{p}% $-Caffarelli-Kohn-Nirenberg inequalities. (Theorems 1.8 and 1.9.) We also derive the best constants and explicit extremal functions for a large family of $L^{2}$ and $L^{p}$ Caffarelli-Kohn-Nirenberg inequalities. (Corollaries 1.1 and 1.2.)

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stability of the $L^{p}$-Poincar\'e inequality for the Lebesgue measure and Gaussian probability measure with explicit geometric dependence and applications to spectral gaps

    math.AP 2026-02 conditional novelty 7.0 of 10

    An explicit geometric stability constant is derived for the L^p-Poincaré inequality on convex domains, yielding a new but partially non-explicit spectral-gap bound for the p-Laplacian.

  2. On the extremal functions of second order uncertainty principles: symmetry and symmetry breaking

    math.AP 2025-08 conditional novelty 7.0 of 10

    In dimensions 2 and 3, the sharp constant in the second-order Hydrogen uncertainty principle is strictly smaller than previously conjectured; a weighted extension has sharp radial extremals.

  3. Sharp anisotropic $L^2$-Caffarelli-Kohn-Nirenberg inequalities associated with the Minkowski functional

    math.AP 2026-07 conditional novelty 6.0 of 10

    Sharp anisotropic L2-CKN inequalities and Heisenberg uncertainty principles hold for the radial derivative associated with any smooth strictly convex body, with explicit extremals and constants matching the Euclidean theory.

Pith tools