\t\t\t\tSpeaker: Alexander Volberg (MSU)<\/p>\n
Title: Beyond the scope of doubling: weighted martingale multipliers and outer measure spaces<\/p>\n
Abstract: A new approach to characterizing the unconditional basis property of martingale differences in weighted $L^2(w d\\nu)$ spaces is given for arbitrary martingales, resulting in a new version with arbitrary and in particular non-doubling reference measure $\\nu$. The approach combines embeddings into outer measure spaces with a core concavity argument of Bellman function type. Specifically, we prove that finiteness of the $A_2$ characteristic of the weight (defined through averages relative to arbitrary reference measure $\\nu$) is equivalent to the boundedness of martingale multipliers. Even in the case of the usual dyadic martingales based on dyadic cubes in $\\mathbb{R}^d$ our result is new because it is dimension free. In the case of general measures, this result is unexpected. For example, a small change in operator breaks the result immediately. This is a joint work with Christoph Thiele and Sergei Treil.\t\t<\/p>\n","protected":false},"excerpt":{"rendered":"
Speaker: Alexander Volberg (MSU) Title: Beyond the scope of doubling: weighted martingale multipliers and outer measure spaces Abstract: A new approach to characterizing the unconditional basis property of martingale differences in weighted $L^2(w d\\nu)$ spaces is given for arbitrary martingales, resulting in a new version with arbitrary and in particular non-doubling reference measure $\\nu$. The […]<\/p>\n","protected":false},"author":103,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-74","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/74","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/users\/103"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=74"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/74\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=74"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=74"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=74"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}