Generalized Hausdorff Operators on K ̇ α , q β , p ℝ and H K ̇ α , q β , p , N ℝ in the Dunkl Settings

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 .

Weighted Lebesgue and central Morrey estimates for -adic multilinear Hausdorff operators and its commutators

UDC 517.9 We establish the sharp boundedness of -adic multilinear Hausdorff operators on the product of Lebesgue and central Morrey spaces associated with both power weights and Muckenhoupt weights. Moreover, the boundedness for the commutators of -adic multilinear Hausdorff operators on the such spaces with symbols in central BMO space is also obtained.