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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.10990 |
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| _version_ | 1866908827930066944 |
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| author | Yang, Meng |
| author_facet | Yang, Meng |
| contents | For $p>1$, we study subordination phenomena for local and non-local regular $p$-energies on metric measure spaces. Under suitable geometric assumptions, we show that if a local regular $p$-energy satisfies a Poincaré inequality together with a cutoff Sobolev inequality with scaling function $Ψ$, then all associated stable-like non-local $p$-energies with scaling functions strictly below $Ψ$ are regular and satisfy the corresponding non-local cutoff Sobolev inequalities. Moreover, if a stable-like non-local regular $p$-energy with scaling function $Ψ$ satisfies the corresponding non-local cutoff Sobolev inequality, then the same conclusion holds for all associated stable-like non-local $p$-energies with scaling functions below $Ψ$. These results provide a non-linear extension of the classical subordination principle beyond the Dirichlet form framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10990 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cutoff Sobolev inequalities for local and non-local $p$-energies on metric measure spaces Yang, Meng Analysis of PDEs Functional Analysis Metric Geometry Probability 31E05, 28A80 For $p>1$, we study subordination phenomena for local and non-local regular $p$-energies on metric measure spaces. Under suitable geometric assumptions, we show that if a local regular $p$-energy satisfies a Poincaré inequality together with a cutoff Sobolev inequality with scaling function $Ψ$, then all associated stable-like non-local $p$-energies with scaling functions strictly below $Ψ$ are regular and satisfy the corresponding non-local cutoff Sobolev inequalities. Moreover, if a stable-like non-local regular $p$-energy with scaling function $Ψ$ satisfies the corresponding non-local cutoff Sobolev inequality, then the same conclusion holds for all associated stable-like non-local $p$-energies with scaling functions below $Ψ$. These results provide a non-linear extension of the classical subordination principle beyond the Dirichlet form framework. |
| title | Cutoff Sobolev inequalities for local and non-local $p$-energies on metric measure spaces |
| topic | Analysis of PDEs Functional Analysis Metric Geometry Probability 31E05, 28A80 |
| url | https://arxiv.org/abs/2602.10990 |