Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$ by Saadi, Faouaz, Daher, Radouan

“…Our aim in this paper is to show that the modulus of smoothness and the $K$-functionals constructed from the Sobolev-type space corresponding to the Dunkl operator are equivalent on the interval $(-1,1)$.…”
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Necessary and Sufficient Conditions for the Boundedness of Dunkl-Type Fractional Maximal Operator in the Dunkl-Type Morrey Spaces by Emin Guliyev, Ahmet Eroglu, Yagub Mammadov

“…We consider the generalized shift operator, associated with the Dunkl operator Λ𝛼(𝑓)(𝑥)=(𝑑/𝑑𝑥)𝑓(𝑥)+((2𝛼+1)/𝑥)((𝑓(𝑥)−𝑓(−𝑥))/2), 𝛼>−1/2. …”
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Boundedness of Multidimensional Dunkl-Hausdorff Operators by Radouan Daher, Faouaz Saadi

“…In the present paper, we introduce the multidimensional Dunkl-Hausdorff operator ℋκ and we give simple sufficient conditions so that these operators be bounded on the weighted lebesgue spaces Lκpℝn and in the Hardy space Hκ1ℝn associated with the Dunkl operators. We also determine the Dunkl-Hausdorff operator ℋκ∗ that is adjoint to ℋκ.…”
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On constraints of the (β-deformed) partition functions with W-representations by Yu-Sen Zhu, Ren Cuo Ji, Min-Li Li, Rui Wang

“…Meanwhile, we obtain a new realization of the Virasoro algebra in terms of the Dunkl operators and the conserved quantities in the rational Calogero model.…”
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Paley and Hardy's inequalities for the Fourier-Dunkl expansions by Anis Elgarna

“…Research limitations/implications – This work is a participation in extending the harmonic analysis associated with the Dunkl operators and it shows the utility of BMO spaces to establish some analytical results. …”
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