{"id":"W2950644276","doi":"10.48550/arxiv.1608.02312","title":"Weighted Fourier inequalities via rearrangements","year":2016,"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":"Western University","funders":"","keywords":"Mathematics; Fourier transform; Simple (philosophy); Mathematical proof; Inequality; Lebesgue integration; Fourier series; Fourier analysis; Pure mathematics; Mathematical analysis; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00356416,0.001236213,0.0009362985,0.002770827,0.0009887443,0.002161224,0.00163943,0.00131303,0.01596917],"category_scores_gemma":[0.01210977,0.000657885,0.002247633,0.001358408,0.003928598,0.007028256,0.004660028,0.004988043,0.00210044],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001847918,"about_ca_system_score_gemma":0.0008786182,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008480884,"about_ca_topic_score_gemma":0.000939281,"domain_scores_codex":[0.9977453,0.0007919683,0.0001732655,0.0004417727,0.0004984526,0.0003491398],"domain_scores_gemma":[0.995926,0.002530321,0.0004784823,0.0004571879,0.0004301788,0.0001778809],"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":[0.00002922205,0.00001048409,0.0001370892,0.00006987391,0.00001192235,0.0001127388,0.0001313891,0.002215354,0.004798235,0.9841707,0.0008460048,0.007466902],"study_design_scores_gemma":[0.00002884751,0.00008172964,0.0004946354,0.00007392459,0.00003086829,0.0002278149,0.0001583987,0.03124211,0.004995535,0.9460025,0.01662309,0.0000404759],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04434936,0.001484871,0.8773377,0.001913333,0.0005413453,0.0001505534,0.0003850751,0.0002037431,0.07363403],"genre_scores_gemma":[0.7374808,0.002692037,0.2187662,0.001664552,0.001183971,0.0008063591,0.0007388298,0.0005751873,0.03609215],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01596917,"threshold_uncertainty_score":0.05342227,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2179085287945161,"score_gpt":0.2802736848985215,"score_spread":0.06236515610400545,"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."}}