8 papers
A new proof of maximal theorem on Heisenberg groups
Chuhan Sun, Zipeng Wang
Given , we define \[\begin{array}{lr} \mathbf{M}_αf(u,v,t) = \sup_{ \mathbf{R} \ni (0,0,0)} {\rm vol} \{\mathbf{R}\}^{α-1} \iiint_\mathbf{R}\left|f [(u,v,t)\odot(ξ,η,τ)^{…
Strong maximal function revisit on Heisenberg group
Chuhan Sun
We prove the -boundedness of the strong maximal operator defined on a Heisenberg group w.r.t an absolutely continuous measure satisfying the product -property.
Stein-Weiss inequality revisit on Heisenberg group
Chuhan Sun, Zipeng Wang
We study a family of fractional integral operators defined on Heisenberg group whose kernels satisfy Zygmund dilation. We give a characterization between a two-weight norm inequali…
Multi-parameter fractional integration on Heisenberg group
Chuhan Sun, Zipeng Wang
We study strong fractional maximal operator and fractional integral operator associated with Zygmund dilation defined on Heisenberg group. Characterizations are established for the…
Hardy-Littlewood-Sobolev inequality revisit on Heisenberg group
Chuhan Sun, Zipeng Wang
We study a family of fractional integral operators defined on Heisenberg groups. The kernels of these operators satisfy Zygmund dilations. We obtain a Hardy-Littlewood-Sobolev type…
On the end-point of Stein-Weiss inequality
Chuhan Sun, Zipeng Wang
This paper has two purposes. First, we show that the classical Stein-Weiss inequality is true for p=1. Second, by considering a family of strong fractional integral operators whose…
Triebel-Lizorkin spaces in Dunkl setting
Chuhan Sun, Zhiming Wang
We establish Triebel-Lizorkin spaces in the Dunkl setting which are associated with finite reflection groups on the Euclidean space. The group structures induce two nonequivalent m…
Weighted -norm inequality of multi-parameter fractional integration
Chuhan Sun, Zipeng Wang
We study a family of strong fractional integral operators whose kernels have singularity on every coordinate subspace. We prove a desired two-weight, L^p-norm inequality provided t…