Displaying similar documents to “Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator”

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.

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).

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.

Gagliardo-Nirenberg inequalities in weighted Orlicz spaces

Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba (2006)

Studia Mathematica

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We derive inequalities of Gagliardo-Nirenberg type in weighted Orlicz spaces on ℝⁿ, for maximal functions of derivatives and for the derivatives themselves. This is done by an application of pointwise interpolation inequalities obtained previously by the first author and of Muckenhoupt-Bloom-Kerman-type theorems for maximal functions.

New Orlicz variants of Hardy type inequalities with power, power-logarithmic, and power-exponential weights

Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba (2012)

Open Mathematics

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We obtain Hardy type inequalities ∫ 0 ∞ M ω r u r ρ r d r ⩽ C 1 ∫ 0 ∞ M u r ρ r d r + C 2 ∫ 0 ∞ M u ' r ρ r d r , and their Orlicz-norm counterparts ω u L M ( ℝ + , ρ ) ⩽ C ˜ 1 u L M ( ℝ + , ρ ) + C ˜ 2 u ' L M ( ℝ + , ρ ) , with an N-function M, power, power-logarithmic and power-exponential weights ω, ρ, holding on suitable dilation invariant supersets of C 0∞(ℝ+). Maximal sets of admissible functions u are described. This paper is based on authors’ earlier abstract results and applies them to particular classes of weights.