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Displaying similar documents to “Two-weight mixed ф-inequalities for the one-sided maximal function”

Two-weight weak type maximal inequalities in Orlicz classes

Luboš Pick (1991)

Studia Mathematica

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Necessary and sufficient conditions are shown in order that the inequalities of the form ϱ ( M μ f > λ ) Φ ( λ ) ≤ C ʃ X Ψ ( C | f ( x ) | ) σ ( x ) d μ , or ϱ ( M μ f > λ ) ≤ C ʃ X Φ ( C λ - 1 | f ( x ) | ) σ ( x ) d μ hold with some positive C independent of λ > 0 and a μ-measurable function f, where (X,μ) is a space with a complete doubling measure μ, M μ is the maximal operator with respect to μ, Φ, Ψ are arbitrary Young functions, and ϱ, σ are weights, not necessarily doubling.

Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator

S. Bloom, R. Kerman (1994)

Studia Mathematica

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Necessary and sufficient conditions are given for the Hardy-Littlewood maximal operator to be bounded on a weighted Orlicz space when the complementary Young function satisfies Δ 2 . Such a growth condition is shown to be necessary for any weighted integral inequality to occur. Weak-type conditions are also investigated.

Weighted norm inequalities on spaces of homogeneous type

Qiyu Sun (1992)

Studia Mathematica

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We give a characterization of the weights (u,w) for which the Hardy-Littlewood maximal operator is bounded from the Orlicz space L_Φ(u) to L_Φ(w). We give a characterization of the weight functions w (respectively u) for which there exists a nontrivial u (respectively w > 0 almost everywhere) such that the Hardy-Littlewood maximal operator is bounded from the Orlicz space L_Φ(u) to L_Φ(w).

Norm inequalities for off-centered maximal operators.

Richard L. Wheeden (1993)

Publicacions Matemàtiques

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Sufficient conditions are derived in order that there exist strong-type weighted norm inequalities for some off-centered maximal functions. The maximal functions are of Hardy-Littlewood and fractional types taken over starlike sets in R. The sufficient conditions are close to necessary and extend some previously known weak-type results.

Weighted L Φ integral inequalities for operators of Hardy type

Steven Bloom, Ron Kerman (1994)

Studia Mathematica

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Necessary and sufficient conditions are given on the weights t, u, v, and w, in order for Φ 2 - 1 ( ʃ Φ 2 ( w ( x ) | T f ( x ) | ) t ( x ) d x ) ≤ Φ 1 - 1 ( ʃ Φ 1 ( C u ( x ) | f ( x ) | ) v ( x ) d x ) to hold when Φ 1 and Φ 2 are N-functions with Φ 2 ∘ Φ 1 - 1 convex, and T is the Hardy operator or a generalized Hardy operator. Weak-type characterizations are given for monotone operators and the connection between weak-type and strong-type inequalities is explored.