scholarly journals Spherical means on the Heisenberg group: Stability of a maximal function estimate

2021 ◽  
Author(s):  
Theresa C. Anderson ◽  
Laura Cladek ◽  
Malabika Pramanik ◽  
Andreas Seeger
Keyword(s):  
Heisenberg Group ◽  
Maximal Function ◽  
Spherical Means ◽  
Function Estimate ◽  
Group Stability

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

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.

Injectivity sets for spherical means on the Heisenberg group

1999 ◽  
Vol 5 (4) ◽  
pp. 363-372 ◽  
Author(s):  
Mark L. Agranovsky ◽  
Rama Rawat
Keyword(s):  
Heisenberg Group ◽  
Spherical Means

scholarly journals Pointwise convergence problem of free Benjamin-Ono-Burgers equation

2022 ◽  
Vol 7 (4) ◽  
pp. 5527-5533
Author(s):  
Fei Zuo ◽  
◽  
Junli Shen ◽  
Keyword(s):  
Maximal Function ◽  
Pointwise Convergence ◽  
Burgers Equation ◽  
Convergence Problem ◽  
Function Estimate ◽  
Almost Everywhere

<abstract><p>In this paper, we show the almost everywhere pointwise convergence of free Benjamin-Ono-Burgers equation in $ H^{s}({\bf{R}}) $ with $ s &gt; 0 $ with the aid of the maximal function estimate.</p></abstract>

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