Weighted Inequalities in Lorentz and Orlicz Spaces

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

Calderón–Zygmund singular integrals in central Morrey–Orlicz spaces

2020 ◽  
Vol 72 (2) ◽  
pp. 235-259
Author(s):  
Lech Maligranda ◽  
Katsuo Matsuoka
Keyword(s):  
Singular Integrals ◽  
Orlicz Spaces

Martingale Rransforms between Hardy-Orlicz Spaces of LΦPredictable Martingales

2012 ◽  
Vol 14 (3) ◽  
pp. 245
Author(s):  
Feng LUO ◽  
Lin YU ◽  
Hongping GUO
Keyword(s):  
Orlicz Spaces
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