2016/02/05 by Luc Deleaval, Deleaval, Luc, Olivier Guédon +4 · 24 citations
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Combinatorics #Convex analysis #Convex function #Convex optimization #Dimension (graph theory) #FOS: Mathematics #Fourth Dimension #Functional Analysis (math.FA) #Geometry #Mathematics #Operator (biology) #Physics #Point processes and geometric inequalities #Pure mathematics #Regular polygon #Series (stratigraphy) #math.FA
paper · pdf · doi:10.48550/arxiv.1602.02015
published in arXiv (Cornell University) (Cornell University) · Version v4 includes several suggestions from the reviewers; section 1.2 has been rewritten to a great extent. Lemma 4.7 (new) allows us to avoid some repetitions later on. Remark 7.14 completes Remark 7.13. Numerous minor edits have been done throughout, and some relevant references added
openalex publication_date 2016/02/05 · arxiv created 2016/09/15 · arxiv updated 2016/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
This survey is based on a series of lectures given by the authors at the\nworking seminar "Convexit 'e et Probabilit 'es" at UPMC Jussieu, Paris, during\nthe spring 2013. It is devoted to maximal inequalities associated to symmetric\nconvex sets in high dimensional linear spaces, a topic mainly developed between\n1982 and 1990 but recently renewed by further advances.\n The series focused on proving for these maximal functions inequalities in\nLp(\ℝn) with bounds independent of the dimension n, for all p\n\∈ (1, +\∞] in the best cases. This program was initiated in 1982 by\nElias Stein, who obtained the first theorem of this kind for the family of\nEuclidean balls in arbitrary dimension. We present several results along this\nline, proved by Bourgain, Carbery and M "uller during the period 1986--1990,\nand a new one due to Bourgain (2014) for the family of cubes in arbitrary\ndimension. We complete the cube case with negative results for the weak type\n(1, 1) constant, due to Aldaz, Aubrun and Iakovlev--Str "omberg between 2009\nand 2013.\n