{"id":465,"date":"2022-02-27T20:55:51","date_gmt":"2022-02-28T04:55:51","guid":{"rendered":"\/wp\/hades\/?p=465"},"modified":"2022-02-27T20:55:51","modified_gmt":"2022-02-28T04:55:51","slug":"trilinear-smoothing-inequalities-and-a-class-of-bilinear-maximal-functions","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2022\/02\/27\/trilinear-smoothing-inequalities-and-a-class-of-bilinear-maximal-functions\/","title":{"rendered":"Trilinear Smoothing Inequalities and a Class of Bilinear Maximal Functions"},"content":{"rendered":"\n\t\t\t\t\n<p>The HADES seminar on Tuesday,&nbsp;<strong>March 1<\/strong> will be at <strong>3:30 pm<\/strong> in <strong>Room 740<\/strong>.<\/p>\n\n\n\n<p><strong>Speaker<\/strong>: Zirui Zhou<\/p>\n\n\n\n<p><strong>Abstract: <\/strong>In this talk, we will present a trilinear smoothing inequality of the form <br> $$\\left|\\int_{\\mathbb R^2} \\prod_{j=0}^2 (f_j\\circ\\varphi_j)(x)\\,\\eta(x)\\,dx\\right|<br> \\leq C \\prod_{j=0}^2 \\|f_j\\|_{W^{p,\\sigma}}$$and two of its applications. Lebesgue space bounds are established for certain maximal bilinear functions. The proof combines the degenerate-case trilinear smoothing inequality with Calder\u00f3n-Zygmund theory. <\/p>\n\n\n\n<p>The second application gives a quantitative nonlinear Roth theorem, which recovers Roth-type theorems proved by Bourgain and Christ-Durcik-Roos. This talk is based on joint work with Michael Christ.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,&nbsp;March 1 will be at 3:30 pm in Room 740. Speaker: Zirui Zhou Abstract: In this talk, we will present a trilinear smoothing inequality of the form $$\\left|\\int_{\\mathbb R^2} \\prod_{j=0}^2 (f_j\\circ\\varphi_j)(x)\\,\\eta(x)\\,dx\\right| \\leq C \\prod_{j=0}^2 \\|f_j\\|_{W^{p,\\sigma}}$$and two of its applications. Lebesgue space bounds are established for certain maximal bilinear functions. The proof [&hellip;]<\/p>\n","protected":false},"author":90,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-465","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/465","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/90"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=465"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/465\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=465"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=465"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=465"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}