{"paper":{"title":"Multipliers in Bessel potential spaces. The case of different sign smooth indices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A.A. Belyaev, A.A. Shkalikov","submitted_at":"2018-01-05T16:51:32Z","abstract_excerpt":"The objective of this paper is to describe the space of multipliers acting from a Bessel potential space $H^s_p(\\mathbb R^n)$ into another space $H^{-t}_q(\\mathbb R^n)$, provided that the smooth indices of these spaces have different signs, i.e. $s, t \\geqslant 0$. This space of multipliers consists of distributions $u$, such that for all $\\varphi \\in H^s_p(\\mathbb R^n)$ the product $\\varphi \\cdot u$ is well-defined and belongs to the space $H^{-t}_q(\\mathbb R^n)$. We succeed to describe this space explicitly, provided that $p \\leqslant q$ and one of the following conditions $$ s \\geqslant t \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01830","kind":"arxiv","version":1},"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"}