scholarly journals A remark on weighted inequalities for general maximal operators

1993 ◽  
Vol 119 (4) ◽  
pp. 1121-1121
Author(s):  
C. P{érez
Keyword(s):  
Maximal Operators ◽  
Weighted Inequalities

Weighted inequalities for the one-sided geometric maximal operators

2011 ◽  
Vol 284 (11-12) ◽  
pp. 1515-1522 ◽  
Author(s):  
Pedro Ortega Salvador ◽  
Consuelo Ramírez Torreblanca
Keyword(s):  
Maximal Operators ◽  
Weighted Inequalities ◽  
The One

Weighted Lorentz norm inequalities for general maximal operators associated with certain families of Borel measures

1998 ◽  
Vol 128 (2) ◽  
pp. 403-424 ◽  
Author(s):  
María Dolores Sarrión Gavilán
Keyword(s):  
Maximal Operator ◽  
Maximal Operators ◽  
Weighted Inequalities ◽  
General Measure ◽  
Norm Inequalities ◽  
Fractional Maximal Operator ◽  
Borel Measures ◽  
The One ◽  
Littlewood Maximal Operator ◽  
Lorentz Norm

Given a certain family ℱ of positive Borel measures and γ ∈ [0, 1), we define a general onesided maximal operatorand we study weighted inequalities inLp,qspaces for these operators. Our results contain, as particular cases, the characterisation of weighted Lorentz norm inequalities for some well-known one-sided maximal operators such as the one-sided Hardy–Littlewood maximal operator associated with a general measure, the one-sided fractional maximal operatorand the maximal operatorassociated with the Cesèro-α averages.

scholarly journals MIXED NORM INEQUALITIES FOR SOME DIRECTIONAL MAXIMAL OPERATORS

2012 ◽  
Vol 86 (3) ◽  
pp. 448-455
Author(s):  
DAH-CHIN LUOR
Keyword(s):  
Harmonic Analysis ◽  
Maximal Functions ◽  
Maximal Operators ◽  
Mixed Norm ◽  
Weighted Inequalities ◽  
Norm Inequalities ◽  
One Dimensional

AbstractMixed norm inequalities for directional operators are closely related to the boundedness problems of several important operators in harmonic analysis. In this paper we prove weighted inequalities for some one-dimensional one-sided maximal functions. Then by applying these results, we establish mixed norm inequalities for directional maximal operators which are defined from these one-dimensional maximal functions. We also estimate the constants in these inequalities.

On the equivalence of weighted inequalities for a class of operators

2011 ◽  
Vol 141 (5) ◽  
pp. 1071-1081 ◽  
Author(s):  
Dah-Chin Luor
Keyword(s):  
Weight Function ◽  
Geometric Mean ◽  
Integral Operators ◽  
Maximal Operators ◽  
Weighted Inequalities

A characterization is obtained on weight function u so that $\smash{T\colon L_{p}^+\mapsto L_{q,u}^+}$ is bounded for 1 < p < ∞ and 0 < q < ∞, where T are integral operators and related maximal operators, and for 0 < p, q < ∞, where T are geometric mean operators and related geometric maximal operators. The equivalence of such weighted inequalities for these operators are established.

Weighted inequalities for Cesàro maximal operators in Orlicz spaces

2005 ◽  
Vol 135 (6) ◽  
pp. 1287-1308 ◽  
Author(s):  
Pedro Ortega Salvador ◽  
Consuelo Ramírez Torreblanca
Keyword(s):  
Orlicz Space ◽  
Integral Inequality ◽  
Orlicz Spaces ◽  
Sufficient Conditions ◽  
Maximal Operators ◽  
Weighted Inequalities ◽  
Ergodic Averages ◽  
Measurable Transformation ◽  
Integrable Functions ◽  
Image Position

Let 0 < α ≤ 1 and let M+α be the Cesàro maximal operator of order α defined by In this work we characterize the pairs of measurable, positive and locally integrable functions (u, v) for which there exists a constant C > 0 such that the inequality holds for all λ > 0 and every f in the Orlicz space LΦ(v). We also characterize the measurable, positive and locally integrable functions w such that the integral inequality holds for every f ∈ LΦ(w). The discrete versions of this results allow us, by techniques of transference, to prove weighted inequalities for the Cesàro maximal ergodic operator associated with an invertible measurable transformation, T, which preserves the measure.Finally, we give sufficient conditions on w for the convergence of the sequence of Cesàro-α ergodic averages for all functions in the weighted Orlicz space LΦ(w).

Two-weighted inequalities for maximal operators related to Schrödinger differential operator

2020 ◽  
Vol 32 (6) ◽  
pp. 1415-1439
Author(s):  
Maria Amelia Vignatti ◽  
Oscar Salinas ◽  
Silvia Hartzstein
Keyword(s):  
Fractional Integral ◽  
Schrödinger Operators ◽  
Finite Measure ◽  
The Other ◽  
Maximal Operators ◽  
Schrodinger Operators ◽  
Homogeneous Type ◽  
Weighted Inequalities ◽  
Spaces Of Homogeneous Type ◽  
Measure Spaces

AbstractWe introduce classes of pairs of weights closely related to Schrödinger operators, which allow us to get two-weight boundedness results for the Schrödinger fractional integral and its commutators. The techniques applied in the proofs strongly rely on one hand, boundedness results in the setting of finite measure spaces of homogeneous type and, on the other hand, Fefferman–Stein-type inequalities that connect maximal operators naturally associated to Schrödinger operators.

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