{"id":"W4319050308","doi":"10.48550/arxiv.2302.00542","title":"$h^1$ boundedness of Localized Operators and Commutators with bmo and lmo","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Harmonic Analysis Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Centre de Recherches Mathématiques","keywords":"Commutator; Smoothness; Maximal function; Singular integral; Bounded mean oscillation; Hardy space; Mathematics; Type (biology); Homogeneous; Space (punctuation); Bounded function; Oscillation (cell signaling); Convolution (computer science); Pure mathematics; Function (biology); Singular integral operators; Operator (biology); Mathematical analysis; Combinatorics; Integral equation; Algebra over a field","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001797412,0.0007548886,0.0005616792,0.001096698,0.000913566,0.00137521,0.001440924,0.0008100769,0.004677851],"category_scores_gemma":[0.003956554,0.0002589234,0.0008589677,0.00043956,0.003507743,0.003103337,0.003719381,0.002202225,0.0005120768],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009586329,"about_ca_system_score_gemma":0.0006568575,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001228732,"about_ca_topic_score_gemma":0.0006411878,"domain_scores_codex":[0.9989594,0.0002340434,0.0000551784,0.0002402713,0.0003067585,0.0002043813],"domain_scores_gemma":[0.9978803,0.0007405184,0.0003875749,0.0002497266,0.0003256178,0.0004162543],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002793458,0.00002366851,0.0004605674,0.00006327266,0.00001049007,0.000153893,0.000367061,0.0009368115,0.006108665,0.9883367,0.0003716929,0.003139304],"study_design_scores_gemma":[0.00002751396,0.0001177879,0.001717839,0.00004246346,0.00002249791,0.0004760013,0.0003750571,0.05935527,0.006958752,0.9257448,0.005117904,0.00004415013],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.362695,0.001600808,0.5689194,0.001663436,0.0002826325,0.00005856591,0.0001729229,0.0002726329,0.0643346],"genre_scores_gemma":[0.9380528,0.000610003,0.04273156,0.0006572429,0.0003191559,0.0001265026,0.0001423851,0.0002182007,0.01714212],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004677851,"threshold_uncertainty_score":0.01564902,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1943838320478515,"score_gpt":0.2744496488545358,"score_spread":0.08006581680668426,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}