{"id":"W1980350398","doi":"10.1016/j.jfa.2005.09.009","title":"Multivariate polynomial inequalities with respect to doubling weights and <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:msub><mml:mi>A</mml:mi><mml:mo>∞</mml:mo></mml:msub></mml:math> weights","year":2005,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Analytic and geometric function theory","field":"Mathematics","cited_by":77,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Unit sphere; Polynomial; Combinatorics; Multivariate statistics; Function (biology); Rank (graph theory); Unit cube; Mathematical analysis; Statistics","routes":{"ca_aff":true,"ca_fund":false,"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":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001888387,0.0004322872,0.0004896515,0.001285042,0.0008258361,0.0004319126,0.0004616824,0.0004811414,0.004160038],"category_scores_gemma":[0.0009539261,0.0004725049,0.001123963,0.001608396,0.0002947091,0.0008091623,0.0002751994,0.0007519037,0.0003590407],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000534285,"about_ca_system_score_gemma":0.0004777006,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004164006,"about_ca_topic_score_gemma":0.0002540221,"domain_scores_codex":[0.9954455,0.0001908551,0.001362454,0.0006193348,0.001700968,0.0006809264],"domain_scores_gemma":[0.9955579,0.001504411,0.001491974,0.0005581363,0.0003569937,0.0005305741],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.003418313,0.0003133131,0.0001126618,0.000153102,0.005668431,0.0001910947,0.001168689,0.006815313,0.0005534397,0.9658564,0.01479003,0.000959165],"study_design_scores_gemma":[0.01049795,0.00484727,0.001867423,0.001248735,0.02144607,0.003363271,0.008300871,0.7666376,0.1190823,0.0360987,0.02330593,0.0033038],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9751316,0.0004546146,0.01587958,0.000896444,0.0005761562,0.00003352929,0.00005792203,0.00006654769,0.006903554],"genre_scores_gemma":[0.9879116,0.0001750157,0.007392974,0.0007061116,0.002363604,0.00004552284,0.00006482683,0.0001168057,0.001223481],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9297578,"threshold_uncertainty_score":0.9997727,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02571899769456282,"score_gpt":0.2540594845510282,"score_spread":0.2283404868564654,"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."}}