Characterizations of reverse weighted inequalities for maximal operators in Orlicz spaces and Stein’s result

2015 ◽  
Vol 147 (2) ◽  
pp. 354-367
Author(s):  
O. Gorosito ◽  
A. M. kanashiro ◽  
G. Pradolini
Keyword(s):  
Orlicz Spaces ◽  
Maximal Operators ◽  
Weighted Inequalities

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).

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 Inequalities in Lorentz and Orlicz Spaces

10.1142/1367 ◽  
1991 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Miroslav Krbec
Keyword(s):  
Orlicz Spaces ◽  
Weighted Inequalities

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.

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