Displaying similar documents to “Two weight function norm inequalities for the Hardy-Littlewood maximal function and the Hilbert transform”

Equivalence of norms in one-sided Hp spaces.

Liliana de Rosa, Carlos Segovia (2002)

Collectanea Mathematica

Similarity:

One-sided versions of maximal functions for suitable defined distributions are considered. Weighted norm equivalences of these maximal functions for weights in the Sawyer's Aq+ classes are obtained.

The Muckenhoupt class A₁(R)

B. Bojarski, C. Sbordone, I. Wik (1992)

Studia Mathematica

Similarity:

It is shown that the Muckenhoupt structure constants for f and f* on the real line are the same.

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...