{"id":"W2115535855","doi":"10.1017/s0308210500003371","title":"Boundedness of the Cesàro averaging operators on Dirichlet spaces","year":2004,"lang":"en","type":"article","venue":"Proceedings of the Royal Society of Edinburgh Section A Mathematics","topic":"Advanced Banach Space Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"University of Alberta","keywords":"Bounded function; Mathematics; Pure mathematics; Dirichlet distribution; Space (punctuation); Operator theory; Mathematical analysis; Computer science","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009698792,0.0003216521,0.0005963635,0.00005568226,0.000297702,0.00003559552,0.0007878637,0.0001829177,0.00005680085],"category_scores_gemma":[0.000850012,0.0001990588,0.0006284707,0.0006537761,0.0005441462,0.0001743957,0.0003250555,0.0004358471,5.066939e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002224696,"about_ca_system_score_gemma":0.00008288254,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003184873,"about_ca_topic_score_gemma":0.000002431967,"domain_scores_codex":[0.9977412,0.00001144127,0.00073539,0.000267134,0.0009273989,0.0003173945],"domain_scores_gemma":[0.9972959,0.0002988133,0.001457356,0.0003646539,0.0005234306,0.00005981167],"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":[0.0003017962,0.005956684,0.005596876,0.01222826,0.001944455,4.411868e-7,0.2314803,0.02120835,0.1498832,0.5022524,0.06874277,0.0004045016],"study_design_scores_gemma":[0.001216443,0.0001843792,0.0001411951,0.002187475,0.0002731791,0.000009570591,0.02770742,0.002780496,0.353811,0.611036,0.0002797563,0.0003730938],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9908282,0.00004611535,0.002978126,0.0009613704,0.0005904592,0.0006761305,0.00001036059,0.00007688061,0.003832351],"genre_scores_gemma":[0.9774038,0.00001876084,0.02082639,0.00008386179,0.0001868981,0.000023139,2.457868e-7,0.00005281207,0.001404052],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2039278,"threshold_uncertainty_score":0.8117384,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01830212039708766,"score_gpt":0.2672319897181471,"score_spread":0.2489298693210594,"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."}}