scholarly journals Uncertainty Inequalities on Laguerre Hypergroup

2012 ◽  
Vol 10 (1) ◽  
pp. 333-351 ◽  
Author(s):  
Rahmouni Atef
Keyword(s):  
Laguerre Hypergroup ◽  
Uncertainty Inequalities

A variety of uncertainty principles for the Dunkl transform on ℝd

2020 ◽  
pp. 2150077
Author(s):  
Fethi Soltani
Keyword(s):  
Dunkl Transform ◽  
Uncertainty Principles ◽  
Local Type ◽  
Heisenberg Type ◽  
Uncertainty Inequalities

In this work, we prove Clarkson-type and Nash-type inequalities in the Dunkl setting on [Formula: see text] for [Formula: see text]-functions. By combining these inequalities, we show Heisenberg-type inequalities for the Dunkl transform on [Formula: see text], and we deduce local-type uncertainty inequalities for the Dunkl transform on [Formula: see text].

scholarly journals Refined Support and Entropic Uncertainty Inequalities

2013 ◽  
Vol 59 (7) ◽  
pp. 4272-4279 ◽  
Author(s):  
Benjamin Ricaud ◽  
Bruno Torresani
Keyword(s):  
Uncertainty Inequalities

The Weak Type (1, 1) Estimates of Maximal Functions on the Laguerre Hypergroup

2010 ◽  
Vol 53 (3) ◽  
pp. 491-502 ◽  
Author(s):  
Jizheng Huang ◽  
Liu Heping
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Maximal Functions ◽  
Laguerre Hypergroup ◽  
Littlewood Maximal Function

AbstractIn this paper, we discuss various maximal functions on the Laguerre hypergroup K including the heat maximal function, the Poisson maximal function, and the Hardy–Littlewood maximal function which is consistent with the structure of hypergroup of K. We shall establish the weak type (1, 1) estimates for these maximal functions. The Lp estimates for p > 1 follow fromthe interpolation. Some applications are included.

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