{"paper":{"title":"One weight inequality for Bergman projection and Calder\\'on operator induced by radial weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.CV","authors_text":"Francisco J. Mart\\'in Reyes, Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a, Pedro Ortega","submitted_at":"2021-05-17T17:28:29Z","abstract_excerpt":"Let $\\omega$ and $\\nu$ be radial weights on the unit disc of the complex plane such that $\\omega$ admits the doubling property $\\sup_{0\\le r<1}\\frac{\\int_r^1 \\omega(s)\\,ds}{\\int_{\\frac{1+r}{2}}^1 \\omega(s)\\,ds}<\\infty$. Consider the one weight inequality\n  \\begin{equation}\\label{ab1}\n  \\|P_\\omega(f)\\|_{L^p_\\nu}\\le C\\|f\\|_{L^p_\\nu},\\quad 1<p<\\infty,\\tag{\\dag}\n  \\end{equation} for the Bergman projection $P_\\omega$ induced by $\\omega$. It is shown that the Muckenhoupt-type condition\n  $$\n  A_p(\\omega,\\nu)=\\sup_{0\\le r<1}\\frac{\\left(\\int_r^1 s\\nu(s)\\,ds \\right)^{\\frac{1}{p}}\\left(\\int_r^1 s\\left(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.08029","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.08029/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"}