Dear all, The next Banach spaces webinar is on Friday September 25 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Paata Ivanisvili North Carolina State Title: Sharpening the triangle inequality in Lp spaces Abstract. The classical triangle inequality in Lp estimates the norm of the sum of two functions in terms of the sums of the norms of these functions. Perhaps one drawback of this estimate is that it does not see how "orthogonal" these functions are. For example, if f and g are not identically zero and they have disjoint supports then the triangle inequality is pretty strict (say for p>1). Motivated by the L2 case, where one has a trivial inequality ||f+g||^2 \leq ||f||^2 + ||g||^2 + 2 |fg|_1, one can think about the quantity |fg|_1 as measuring the "overlap" between f and g. What is the correct analog of this estimate in Lp for p different than 2? My talk will be based on a joint work with Carlen, Frank and Lieb where we obtain one extension of this estimate in Lp, thereby proving and improving the suggested possible estimates by Carbery, and another work with Mooney where we further refine these estimates. The estimates will be provided for all real p's. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule October 2: Anna Pelczar-Barwacz, Jagiellonian University Thank you, and best regards, Bunyamin Sari