Extremal sequences for the Bellman function of three variables of the dyadic maximal operator related to Kolmogorov’s inequality

2019 ◽  
Vol 372 (9) ◽  
pp. 6315-6342
Author(s):  
Eleftherios N. Nikolidakis
Keyword(s):  
Maximal Operator ◽  
Bellman Function

A weighted weak-type bound for Haar multipliers

2018 ◽  
Vol 148 (3) ◽  
pp. 643-658
Author(s):  
Adam Osȩkowski
Keyword(s):  
Maximal Operator ◽  
Function Method ◽  
Dual Problem ◽  
Weak Type ◽  
Analogous Result ◽  
Type Inequality ◽  
Bellman Function ◽  
Weak Type Inequality ◽  
Image Position

We study a weighted maximal weak-type inequality for Haar multipliers that can be regarded as a dual problem of Muckenhoupt and Wheeden. More precisely, if Tε is the Haar multiplier associated with the sequence ε with values in [−1, 1], and is the r-maximal operator, then for any weight w and any function f on [0, 1) we havefor some constant Cr depending only on r. We also show that the analogous result does not hold if we replace by the dyadic maximal operator Md. The proof rests on the Bellman function method; using this technique we establish related weighted Lp estimates for p close to 1, and then deduce the main result by extrapolation arguments.

Extremal Sequences for the Bellman Function of the Dyadic Maximal Operator and Applications to the Hardy Operator

2017 ◽  
Vol 69 (6) ◽  
pp. 1364-1384
Author(s):  
Eleftherios Nikolaos Nikolidakis
Keyword(s):  
Maximal Operator ◽  
Hardy Operator ◽  
Bellman Function

AbstractWe prove that the extremal sequences for the Bellman function of the dyadic maximal operator behave approximately as eigenfunctions of this operator for a specific eigenvalue. We use this result to prove the analogous one with respect to the Hardy operator.

The maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series

2008 ◽  
Vol 45 (3) ◽  
pp. 321-331
Author(s):  
István Blahota ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Hardy Space ◽  
Maximal Operator ◽  
Fejér Means

In this paper we prove that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series is not bounded from the Hardy space H2/3 ( G2 ) to the space L2/3 ( G2 ).

scholarly journals Weighted norm inequalities for a general maximal operator

1988 ◽  
Vol 26 (1-2) ◽  
pp. 327-340 ◽  
Author(s):  
Francisco J. Ruiz ◽  
Jose L. Torrea
Keyword(s):  
Maximal Operator ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities
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