{"paper":{"title":"Estimates for Schr\\\"{o}dinger Groups and Imaginary Power Operators on Weak Hardy Spaces Associated with Non-negative Self-adjoint Operators and Ball Quasi-Banach Function Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Wenhua Wang, Xiong Liu","submitted_at":"2025-08-19T15:12:51Z","abstract_excerpt":"Let $(\\mathbb{X},d,\\mu)$ be a doubling metric measure space, $L$ a non-negative self-adjoint operator on $L^2(\\mathbb{X})$ satisfying the Davies-Gaffney estimate, and $X(\\mathbb{X})$ a ball quasi-Banach function space on $\\mathbb{X}$ satisfying some mild assumptions with $p\\in(0,\\infty)$ and $s_0\\in(0,\\min\\{p,1\\}]$. In this article, the authors study the weak Hardy space $WH_{X,L}(\\mathbb{X})$ associated with $L$ and $X(\\mathbb{X})$, and then give the atomic and molecular decompositions of $WH_{X,L}(\\mathbb{X})$. As applications, the authors establish the boundedness estimate of Schr\\\"{o}dinge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.13913","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/2508.13913/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"}