Korean J. Math. Vol. 26 No. 1 (2018) pp.103-127
DOI: https://doi.org/10.11568/kjm.2018.26.1.103

Hausdorff operators on weighted Lorentz spaces

Main Article Content

Qinxiu Sun
Dashan Fan
Hongliang Li


This paper is dedicated to studying some Hausdorff operators on the Heisenberg group $\mathbb{H}^{n}$. The sharp bounds on the strong-type weighted Lorentz spaces $\Lambda _{u}^{p}(w)$ and the weak-type weighted Lorentz spaces $ \Lambda _{u}^{p,\infty }(w)$ are investigated. Especially, the results cover the classical power weighted space $L_{\alpha}^{p,q}$. The results are also extended to the product spaces $\Lambda _{u_{1}}^{p_{1}}(w_{1})\times \Lambda_{u_{2}}^{p_{2}}(w_{2})$, especially for $L_{\alpha_{1}}^{p_{1},q_{1}}\times L_{\alpha _{2}}^{p_{2},q_{2}}$. Our proofs are quite different from those in previous documents since the duality principle, and some well-known inequalities concerning the weights are adopted. The results recover the existing results as well as we obtain new results in the new and old settings.

Article Details

Supporting Agencies

National Natural Science Foundation of China (11401530 11461033) NaturalScience Foundation of Zhejiang Province of China (LQ13A010018).


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