The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “The level function in rearrangement invariant spaces.”

The converse of the Hölder inequality and its generalizations

Janusz Matkowski (1994)

Studia Mathematica

Similarity:

Let (Ω,Σ,μ) be a measure space with two sets A,B ∈ Σ such that 0 < μ (A) < 1 < μ (B) < ∞ and suppose that ϕ and ψ are arbitrary bijections of [0,∞) such that ϕ(0) = ψ(0) = 0. The main result says that if ʃ Ω x y d μ ϕ - 1 ( ʃ Ω ϕ x d μ ) ψ - 1 ( ʃ Ω ψ x d μ ) for all μ-integrable nonnegative step functions x,y then ϕ and ψ must be conjugate power functions. If the measure space (Ω,Σ,μ) has one of the following properties: (a) μ (A) ≤ 1 for every A ∈ Σ of finite measure; (b) μ (A) ≥ 1 for every A ∈ Σ of positive measure, then...

Remarks on the Istratescu measure of noncompactness.

Janusz Dronka (1993)

Collectanea Mathematica

Similarity:

In this paper we give estimations of Istratescu measure of noncompactness I(X) of a set X C lp(E1,...,En) in terms of measures I(Xj) (j=1,...,n) of projections Xj of X on Ej. Also a converse problem of finding a set X for which the measure I(X) satisfies the estimations under consideration is considered.