Journal of Lie Theory

no. 1
Dunkl Operators on Rd and Uncentered Maximal Function
Journal of Lie Theory, Volume 20 (2010) no. 1, pp. 113-125
We consider Dunkl theory on Rd associated to a finite reflection group G. We establish first an estimate for the Dunkl translation of the characteristic function of a closed ball with radius ε > 0 centered at 0. Second, we prove that the uncentered maximal function associated with the Dunkl operators is of weak-type (1, 1). We finally obtain that it is strong-type (p, p) for 1 p ≤ +∞.
DOI: 10.5802/jolt.589
Classification: 42B10, 42B25, 44A15, 44A35
Keywords: Dunkl operators, Dunkl transform, Dunkl translations, uncentered maximal function 
@article{JOLT_2010_20_1_a7,
     author = {C. Abdelkefi},
     title = {Dunkl {Operators} on {R\protect\textsuperscript{d}} and {Uncentered} {Maximal} {Function}},
     journal = {Journal of Lie Theory},
     pages = {113--125},
     year = {2010},
     volume = {20},
     number = {1},
     doi = {10.5802/jolt.589},
     zbl = {1198.42008},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.589/}
}
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C. Abdelkefi. Dunkl Operators on Rd and Uncentered Maximal Function. Journal of Lie Theory, Volume 20 (2010) no. 1, pp. 113-125. doi: 10.5802/jolt.589

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