Boundedness of bilinear Dunkl–Hausdorff operators on products of Lebesgue and Morrey spaces

Abstract

We obtain the necessary and sufficient conditions for the bilinear Dunkl–Hausdorff operators on the product Lebesgue spaces and (central) Morrey spaces. We also obtain the sharp constant for the bilinear Dunkl–Hausdorff operators on the weighted Lebesgue spaces $L_k^p(1\le p<\mathrm{\infty })$ when the matrix A in the definition of operators is a scalar matrix.

Keywords:

• Hausdorff operator
• bilinear Dunkl–Hausdorff operator
• Morrey space

2010 Mathematics Subject Classifications:

• 44A15
• 42B35
• 26D15

Acknowledgments

The authors would like to express their sincerely thanks to the referee for his/her valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research was supported by National Natural Science Foundation of China (Grant Nos. 11971295, 11871108) and Natural Science Foundation of Shanghai (No. 19ZR1417600).