{"paper":{"title":"$L^p$ estimates for fractional schrodinger operators with kato class potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ming Wang, Quan Zheng, Shanlin Huang, Zhiwen Duan","submitted_at":"2015-11-25T12:53:34Z","abstract_excerpt":"Let $\\alpha>0$, $H=(-\\triangle)^{\\alpha}+V(x)$, $V(x)$ belongs to the higher order Kato class $K_{2\\alpha}(\\mathbbm{R}^n)$. For $1\\leq p\\leq \\infty$, we prove a polynomial upper bound of $\\|e^{-itH}(H+M)^{-\\beta}\\|_{L^p, L^p}$ in terms of time $t$. Both the smoothing exponent $\\beta$ and the growth order in $t$ are almost optimal compared to the free case. The main ingredients in our proof are pointwise heat kernel estimates for the semigroup $e^{-tH}$. We obtain a Gaussian upper bound with sharp coefficient for integral $\\alpha$ and a polynomial decay for fractal $\\alpha$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08041","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}