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Chuhan Sun

Publications and source records attributed to Chuhan Sun.

8 recordsLinked to original sources
arXiv2026

A new proof of maximal theorem on Heisenberg groups

Given $0\leqα<1$, we define \[\begin{array}{lr} \mathbf{M}_αf(u,v,t) = \sup_{ \mathbf{R} \ni (0,0,0)} {\rm vol} \{\mathbf{R}\}^{α-1} \iiint_\mathbf{R}\left|f [(u,v,t)\odot(ξ,η,τ)^{-1}]\right|dξdηdτ\end{array}\] where $\mathbf{R}\subset\mathbb{R}^{2n+1}$ is a rectangle parallel to the coordinates. Moreover, $\odot$ denotes the multiplication law on a real Heisenberg group. The $\mathbf{L}^p$-boundedness of $\mathbf{M}_0$ has been previously proved by M. Christ. We show $\mathbf{M}_α\colon\mathbf{L}^p(\mathbb{R}^{2n+1}) \to \mathbf{L}^q(\mathbb{R}^{2n+1})$ for $α={1\over p}-{1\over q},~ 1<p\leq q<\infty$ by applying a geometric covering lemma due to Córdoba and Fefferman.

math.CA↗
arXiv2025

Stein-Weiss inequality revisit on Heisenberg group

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 inequality and the necessary constraints by considering the weights to be suitable powers. As a result, we obtain a Stein-Weiss inequality on Heisenberg group.

math.CA↗
arXiv2025

On the end-point of Stein-Weiss inequality

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 kernels have singularity on every coordinate subspace, we extend this end-point result to the multi-parameter setting.

math.CA↗
arXiv2025

Triebel-Lizorkin spaces in Dunkl setting

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 metrics: the Euclidean metric and the Dunkl metric. In this paper, the L^2 space and the Dunkl-Calderon-Zygmund singular integral operator in the Dunkl setting play a fundamental role. The main tools used in this paper are as follows: (i) the Dunkl-Calderon-Zygmund singular integral operator and a new Calderon reproducing formula in L^2 with the Triebel-Lizorkin space norms; (ii) new test functions in terms of the L^2 functions and distributions; (iii) the Triebel-Lizorkin spaces in the Dunkl setting which are defined by the wavelet-type decomposition with norms and the analogous atomic decomposition of the Hardy spaces.

math.CA↗