Refined general weighted $L^{p}$-Hardy and Caffarelli-Kohn-Nirenberg type inequalities and identities related to the Baouendi-Grushin operator
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| Format: | Preprint |
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2025
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| _version_ | 1866911188326023168 |
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| author | Yessirkegenov, Nurgissa Zhangirbayev, Amir |
| author_facet | Yessirkegenov, Nurgissa Zhangirbayev, Amir |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_18440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Refined general weighted $L^{p}$-Hardy and Caffarelli-Kohn-Nirenberg type inequalities and identities related to the Baouendi-Grushin operator Yessirkegenov, Nurgissa Zhangirbayev, Amir Functional Analysis 26D10, 35J70 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. |
| title | Refined general weighted $L^{p}$-Hardy and Caffarelli-Kohn-Nirenberg type inequalities and identities related to the Baouendi-Grushin operator |
| topic | Functional Analysis 26D10, 35J70 |
| url | https://arxiv.org/abs/2504.18440 |