scholarly journals Estimates for the Hardy–Littlewood maximal function on the Heisenberg group

2005 ◽  
Vol 103 (2) ◽  
pp. 199-205 ◽  
Author(s):  
Jacek Zienkiewicz
Keyword(s):  
Heisenberg Group ◽  
Maximal Function ◽  
Littlewood Maximal Function

scholarly journals The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xiang Li ◽  
Xingsong Zhang
Keyword(s):  
Heisenberg Group ◽  
Maximal Function ◽  
Operator Norm ◽  
Littlewood Maximal Function ◽  
Weak Norm

In this article, we define a kind of truncated maximal function on the Heisenberg space by M γ c f x = sup 0 < r < γ 1 / m B x , r ∫ B x , r f y d y . The equivalence of operator norm between the Hardy-Littlewood maximal function and the truncated maximal function on the Heisenberg group is obtained. More specifically, when 1 < p < ∞ , the L p norm and central Morrey norm of truncated maximal function are equal to those of the Hardy-Littlewood maximal function. When p = 1 , we get the equivalence of weak norm L 1 ⟶ L 1 , ∞ and M ̇ 1 , λ ⟶ W ̇ M 1 , λ . Those results are generalization of previous work on Euclid spaces.

scholarly journals On the lacunary spherical maximal function on the Heisenberg group

2021 ◽  
Vol 280 (3) ◽  
pp. 108832
Author(s):  
Pritam Ganguly ◽  
Sundaram Thangavelu
Keyword(s):  
Heisenberg Group ◽  
Maximal Function

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.

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