Some results of reverses Young's inequalities


Yonghui Ren, Pengtong Li




In this paper, we present some refinements of reverse Young's inequalities. Among other results, a refinement of reverse operator Young inequalities says A∇ v B + 2λ(A∇B − A♯B) ≤ m∇ λ M m♯ λ M A♯ v B, where 0 < mI ≤ A, B ≤ MI, λ = min{v, 1 − v} and v ∈ [0, 1], extending a key result in [J. Math. Anal. Appl. 465 (2018) 267-280] and [Linear Multilinear Algebra 67 (2019) 1567-1578]. Furthermore, we give a reverse of Young's inequalities due to [Math. Slovaca 70 (2020), 453-466]. Moreover, we give a generalization of reverse Young-type inequality, and we also show a new Young-type inequality which is either better or not uniformly better than the main results in [Rocky Mountain J. Math. 46 (2016), 1089-1105]. As applications of these results, we obtain some inequalities for operators, Hilbert-Schmidt norms, unitarily invariant norms and determinants.