Hadamard–Landau inequalities in uniformly convex spaces

Abstract

The inequalityfor fεLp(− ∞, ∞)or Lp(0, ∞) (1≤p ≤ ∞), and its extensionfor T an Hermitian or dissipative linear operator, in general unbounded, on a Banach space X, for xεX, have been considered by many authors. In particular, forms of inequality (1) have been given by Hadamard(7), Landau(15), and Hardy and Little-wood(8),(9). The second inequality has been discussed by Kallman and Rota(11), Bollobás (2) and Kato (12), and numerous further references may be found in the recent papers of Kwong and Zettl(i4) and Bollobás and Partington(3).