When Is Lr(R) Contained in Lp(R) + Lq(R) ?

Jean-Baptiste Hiriart-Urruty (1) , Patrice Lassère (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We prove a necessary and sufficient condition on the exponents p, q, r ≥ 1 such that Lr (R) ⊂ Lp(R)+Lq (R). In doing so, we explore the structure of Lp(R) + Lq (R) as a normed vector space.

Domaines: Mathématiques [math]

Jean-Baptiste Hiriart-Urruty, Patrice Lassère. When Is Lr(R) Contained in Lp(R) + Lq(R) ?. The American Mathematical Monthly, 2013, 120 (1), p. 55-61. ⟨10.4169/amer.math.monthly.120.01.055⟩. ⟨hal-00966086⟩