Variation Inequality for the Two-Dimensional Discrete Hardy–Littlewood Maximal Function

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Fayou Zhao ◽  
Hongxiu Zhou
Keyword(s):  
Maximal Function ◽  
Two Dimensional ◽  
Littlewood Maximal Function ◽  
Variation Inequality

scholarly journals A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Feng Liu ◽  
Lei Xu
Keyword(s):  
Bounded Variation ◽  
Sobolev Spaces ◽  
Maximal Function ◽  
Maximal Operator ◽  
Functions Of Bounded Variation ◽  
Two Dimensional ◽  
Littlewood Maximal Function ◽  
Regularity Properties ◽  
Littlewood Maximal Operator

We investigate the regularity properties of the two-dimensional one-sided Hardy-Littlewood maximal operator. We point out that the above operator is bounded and continuous on the Sobolev spaces Ws,p(R2) for 0≤s≤1 and 1<p<∞. More importantly, we establish the sharp boundedness and continuity for the discrete two-dimensional one-sided Hardy-Littlewood maximal operator from l1(Z2) to BV(Z2). Here BV(Z2) denotes the set of all functions of bounded variation on Z2.

The Hardy–Littlewood maximal function

2014 ◽  
pp. 187-188
Author(s):  
Omar El-Fallah ◽  
Karim Kellay ◽  
Javad Mashreghi ◽  
Thomas Ransford
Keyword(s):  
Maximal Function ◽  
Littlewood Maximal Function

scholarly journals A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function

2002 ◽  
Vol 65 (2) ◽  
pp. 253-258 ◽  
Author(s):  
Hitoshi Tanaka
Keyword(s):  
Sobolev Space ◽  
Maximal Function ◽  
60Th Birthday ◽  
One Dimensional ◽  
Partial Derivatives ◽  
First Order ◽  
Littlewood Maximal Function ◽  
The One ◽  
Derivatives Of

Dedicated to Professor Kôzô Yabuta on the occasion of his 60th birthdayJ. Kinnunen proved that of P > 1, d ≤ 1 and f is a function in the Sobolev space W1,P(Rd), then the first order weak partial derivatives of the Hardy-Littlewood maximal function ℳf belong to LP(Rd). We shall show that, when d = 1, Kinnunen's result can be extended to the case where P = 1.

A note on the one-dimensional maximal function

1989 ◽  
Vol 111 (3-4) ◽  
pp. 325-328 ◽  
Author(s):  
Antonio Bernal
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Type Inequality ◽  
Best Constant ◽  
Weak Type Inequality ◽  
One Dimensional ◽  
Littlewood Maximal Function ◽  
The One

SynopsisIn this note, we consider the Hardy-Littlewood maximal function on R for arbitrary measures, as was done by Peter Sjögren in a previous paper. We determine the best constant for the weak type inequality.

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