{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101503"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101503","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Multilinear operators in harmonic analysis: Methods and applications","abstract":"We first give a survey on multilinear Hilbert transforms. Then we study several variants of bilinear Hilbert transform such as bilinear Hilbert transform along two polynomials, discrete (integer) bilinear Hilbert transform along polynomials, finite field version of bilinear Radon transform, a hybrid of bilinear Hilbert transform and the paraproduct, etc. Our aim is to find operator norms of these operators: showing that they are finite or have certain decay. Applications in Roth type theorems will also be given.","abstract_html":"We first give a survey on multilinear Hilbert transforms. Then we study several variants of bilinear Hilbert transform such as bilinear Hilbert transform along two polynomials, discrete (integer) bilinear Hilbert transform along polynomials, finite field version of bilinear Radon transform, a hybrid of bilinear Hilbert transform and the paraproduct, etc. Our aim is to find operator norms of these operators: showing that they are finite or have certain decay. Applications in Roth type theorems will also be given.","abstract_has_math":false,"creators":["Dong, Dong"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Ford, Kevin","Li, Xiaochun","Erdogan, M. 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Then we study several variants of bilinear Hilbert transform such as bilinear Hilbert transform along two polynomials, discrete (integer) bilinear Hilbert transform along polynomials, finite field version of bilinear Radon transform, a hybrid of bilinear Hilbert transform and the paraproduct, etc. Our aim is to find operator norms of these operators: showing that they are finite or have certain decay. Applications in Roth type theorems will also be given.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms","The student, Dong Dong, accepted the attached license on 2018-06-22 at 11:36.","The student, Dong Dong, submitted this Dissertation for approval on 2018-06-22 at 11:44.","This Dissertation was approved for publication on 2018-06-22 at 14:41.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12661 on 2018-09-27 at 10:45:31","Made available in DSpace on 2018-09-27T16:17:31Z (GMT). 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Then we study several variants of bilinear Hilbert transform such as bilinear Hilbert transform along two polynomials, discrete (integer) bilinear Hilbert transform along polynomials, finite field version of bilinear Radon transform, a hybrid of bilinear Hilbert transform and the paraproduct, etc. Our aim is to find operator norms of these operators: showing that they are finite or have certain decay. Applications in Roth type theorems will also be given.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms","The student, Dong Dong, accepted the attached license on 2018-06-22 at 11:36.","The student, Dong Dong, submitted this Dissertation for approval on 2018-06-22 at 11:44.","This Dissertation was approved for publication on 2018-06-22 at 14:41.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12661 on 2018-09-27 at 10:45:31","Made available in DSpace on 2018-09-27T16:17:31Z (GMT). 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