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arXiv · 2504.18440

Refined general weighted $L^{p}$-Hardy and Caffarelli-Kohn-Nirenberg type inequalities and identities related to the Baouendi-Grushin operator

Nurgissa Yessirkegenov·Amir Zhangirbayev
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Abstract

In this paper, we present a sufficient condition on a pair of nonnegative weights $v$ and $w$ such that we have a general weighted $L^{p}$-Hardy type identity. The result, for a certain choice of weights, gives weighted $L^{p}$-Hardy type inequalities and identities with explicit remainder terms, thereby improving previously known results. Furthermore, we obtain the corresponding general weighted Caffarelli-Kohn-Nirenberg type inequality with remainder terms, which, as a result, imply Heisenberg-Pauli-Weyl type inequalities.

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Nurgissa Yessirkegenov, Amir Zhangirbayev. 2025-04-25. Refined general weighted $L^{p}$-Hardy and Caffarelli-Kohn-Nirenberg type inequalities and identities related to the Baouendi-Grushin operator. https://arxiv.org/abs/2504.18440

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