{"paper":{"title":"Pseudodifferential operators with symbols in the H\\\"ormander class $S^0_{\\alpha,\\alpha}$ on $\\alpha$-modulation spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Naohito Tomita, Tomoya Kato","submitted_at":"2017-07-31T03:39:39Z","abstract_excerpt":"In this paper, we study the boundedness of pseudodifferential operators with symbols in the H\\\"ormander class $S^0_{\\rho,\\rho}$ on $\\alpha$-modulation spaces $M_{p,q}^{s,\\alpha}$, and consider the relation between $\\alpha$ and $\\rho$. In particular, we show that pseudodifferential operators with symbols in $S^0_{\\alpha,\\alpha}$ are bounded on all $\\alpha$-modulation spaces $M^{s,\\alpha}_{p,q}$, for arbitrary $s\\in\\mathbb{R}$ and for the whole range of exponents $0 < p,q \\leq \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09710","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"}