Landau-type extremal problem for the triple vertical bar vertical bar f vertical bar vertical bar(infinity), vertical bar vertical bar f 'vertical bar vertical bar(p), vertical bar vertical bar f ''vertical bar vertical bar(infinity) on a finite inte

摘要

For any fixed finite interval I = [a, b] and any p, 1 less than or equal to p less than or equal to infinity, we prove that every extremal function to the problem parallel tofparallel to(Linfinity(I)) less than or equal to1, parallel tof"parallel to(Linfinity)(I) less than or equal to 4, parallel tof'parallel to(Lp(I)) --> sup is a perfect parabolic spline, whose extrema, excluding one at most, take the absolute value 1. (C) 2003 Elsevier Science (USA). All rights reserved. [References: 9]