The Dunkl-Hausdorff operator is bounded on the real Hardy space

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

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“…It started twenty years ago with Dunkl's seminal work in [7] and was further developed by several mathematicians. In the frame of extending these results to the context of Dunkl theory, we have introduced and studied recently in [8] the Dunkl-Hausdorff operators in the one-dimensional case on the spaces L p κ (R) and H 1 κ (R). Now, we are going to study the multidimensional Dunkl-Hausdorff operators in the spirit of those in [3,5].…”

Section: Introductionmentioning

confidence: 99%

Boundedness of Multidimensional Dunkl-Hausdorff Operators

Daher

Saadi

2020

Journal of Function Spaces

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“…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%