Some families of operator norm inequalities

Abstract

We consider the function f α,on the interval (0, ∞), where α = (a 1 , a 2 , . . . , a n ),, Hiai and Kosaki define the relation using positive definiteness for functions f and g with some suitable conditions and they have proved this relation implies the operator norm inequality associated with functions f and g. In this paper, we give some conditions for α ′ , β ′ ∈ R m to hold the relation f α,β (t) f α ′ ,β ′ (t).

Bochner–Riesz operators in grand lebesgue spaces

“…. , n. In the recent article [3] it is proved that (1.3) holds true with C = α, σ = n. Moreover, in this case one has…”