Sharp Lorentz-norm estimates for dyadic-like maximal operators

2021 ◽  
Vol 257 (1) ◽  
pp. 87-110
Author(s):  
Adam Osękowski ◽  
Mateusz Rapicki
Keyword(s):  
Maximal Operators ◽  
Norm Estimates ◽  
Lorentz Norm

scholarly journals Local Lower Norm Estimates for Dyadic Maximal Operators and Related Bellman Functions

2016 ◽  
Vol 27 (3) ◽  
pp. 1940-1950 ◽  
Author(s):  
Antonios D. Melas ◽  
Eleftherios N. Nikolidakis
Keyword(s):  
Maximal Operators ◽  
Norm Estimates ◽  
Bellman Functions

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 Estimates for Compositions of Maximal Operators with Singular Integrals

2013 ◽  
Vol 56 (4) ◽  
pp. 801-813 ◽  
Author(s):  
Richard Oberlin
Keyword(s):  
Singular Integrals ◽  
Weak Type ◽  
Operator Norm ◽  
Maximal Operators ◽  
Multiplier Operator ◽  
Norm Estimates ◽  
Variation Norm

Abstract.We prove weak-type (1, 1) estimates for compositions of maximal operators with singular integrals. Our main object of interest is the operator Δ*Ψ where Δ* is Bourgain’s maximal multiplier operator and is the sum of several modulated singular integrals; here our method yields a significantly improved bound for the Lq operator norm when 1 < q < 2. We also consider associated variation-norm estimates.

Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2877-2889 ◽  
Author(s):  
Amir Sanatpour ◽  
Mostafa Hassanlou
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Essential Norm ◽  
Necessary And Sufficient Conditions ◽  
Norm Estimates ◽  
Type Spaces ◽  
Necessary And Sufficient

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

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