scholarly journals Equivalence of <i>K</i>-Functionals and Modulus of Smoothness Generated by a Generalized Dunkl Operator on the Real Line

2015 ◽  
Vol 05 (06) ◽  
pp. 367-376
Author(s):  
Reem Fahad Al Subaie ◽  
Mohamed Ali Mourou
Keyword(s):  
Real Line ◽  
Modulus Of Smoothness ◽  
Dunkl Operator ◽  
The Real

scholarly journals Dunkl Translation and Uncentered Maximal Operator on the Real Line

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Chokri Abdelkefi ◽  
Mohamed Sifi
Keyword(s):  
Characteristic Function ◽  
Real Line ◽  
Maximal Operator ◽  
Weak Type ◽  
Dunkl Operator ◽  
The Real

We establish estimates of the Dunkl translation of the characteristic functionχ[−ɛ,ɛ],ɛ>0, and we prove that the uncentered maximal operator associated with the Dunkl operator is of weak type(1,1). As a consequence, we obtain theLp-boundedness of this operator for1<p≤+∞.

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