{"paper":{"title":"$L^p$-$L^q$ Fourier multipliers and Hausdorff-Young-Paley inequalities on Riemannian symmetric spaces of noncompact type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Michael Ruzhansky, Tapendu Rana","submitted_at":"2024-09-26T15:45:24Z","abstract_excerpt":"Our primary objective in this article is to establish H\\\"ormander type $L^p \\rightarrow L^q$ Fourier multiplier theorems in the context of noncompact type Riemannian symmetric spaces $\\mathbb{X}$ of arbitrary rank for the range $1 < p \\leq 2 \\leq q < \\infty$. As a consequence of the Fourier multiplier theorem, we also derive a spectral multiplier theorem on $\\mathbb{X}$. We then apply this theorem to prove $L^p \\rightarrow L^q$ boundedness for functions of the Laplace-Beltrami operator and to obtain embedding theorems and operator estimates for the potentials and heat semigroups. Additionally,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.17969","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.17969/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}