The Dunkl-Hausdorff operators and the Dunkl continuous wavelets transform

Daher, Radouan; Saadi, Faouaz

doi:10.1007/s11868-020-00351-1

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Cited by 7 publications

(2 citation statements)

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“…The Dunkl-Hausdorff operator H α (see [6][7][8][9]) acting on L 1 α ðℝÞ generated by a function φ belonging to L 1 ðℝÞ is defined directly as:…”

Section: Introductionmentioning

confidence: 99%

Generalized Hausdorff Operators on ${\dot{K}}_{α, q}$

Saadi

Tyr

Daher

2021

Journal of Function Spaces

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In the present paper, we obtain some new results, and we generalize some known results for the Hausdorff operators. We have studied the generalized Hausdorff operators H α , φ on the Dunkl-type homogeneous weighted Herz spaces K ̇ α , q β , p ℝ and Dunkl Herz-type Hardy spaces H K ̇ α , q β , p , N ℝ . We have determined simple sufficient conditions for these operators to be bounded on these spaces. As applications, we provide necessary and sufficient conditions for generalized Cesàro operator to be bounded on K ̇ α , q β , p ℝ and Hardy inequality for K ̇ α , q β , p ℝ .

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“…The Dunkl-Hausdorff operator H α (see [6][7][8][9]) acting on L 1 α ðℝÞ generated by a function φ belonging to L 1 ðℝÞ is defined directly as:…”

Section: Introductionmentioning

confidence: 99%

Generalized Hausdorff Operators on ${\dot{K}}_{α, q}$

Saadi

Tyr

Daher

2021

Journal of Function Spaces

Self Cite

View full text Add to dashboard Cite

show abstract

“…Coming back to the Dunkl-Hausdorff operator H α,φ , its L 1 α (R) boundedness has been proved in [4] whereas L p α (R) boundedness is obtained in [6] and in each case, a sufficient condition has been provided. We, in this paper, generalize these results by providing a characterization for the L p v (R) boundedness of H α,φ and for a certain type of weight v, we provide the precise value of the norm H α,φ L p v (R)→L p v (R) .…”

Section: Introductionmentioning

confidence: 99%