arXiv subjects

Wenna Lu

Publications and source records attributed to Wenna Lu.

4 recordsLinked to original sources

arXiv2023

A characterization of mixed $\lambda$-central $\mathrm{BMO}$ space via the commutators of Hardy type operators

In this paper, we give a characterization of mixed $\lambda$-central bounded mean oscillation space $\mathrm{CBMO}^{\vec{q},\lambda}(\mathbb{R}^{n})$ via the boundedness of the commutators of $n$-dimensional Hardy operator $\mathcal{H}$ and its dual operator $\mathcal{H}^{*}$ on mixed Lebesgue space $L^{\vec{p}}(\mathbb{R}^{n})$. In addition, we also establish the boundedness of commutators $\mathcal{H}_{b}$ and $\mathcal{H}^{*}_{b}$ generated with $\mathrm{CBMO}^{\vec{q},\lambda}(\mathbb{R}^{n})$ function $b$ on mixed $\lambda$-central Morrey space $\mathcal{B}^{\vec{q},\lambda}(\mathbb{R}^{n})$, respectively.

math.FA↗

arXiv2023

Characterizations of the mixed central Campanato spaces via the commutator operators of Hardy type

The purpose of this paper is to establish some characterizations of mixed central Campanato space $\mathfrak{C}^{\vec{p},\lambda}(\mathbb{R}^{n})$, via the boundedness of the commutator operators of Hardy type. Unlike the case $\lambda\geq0$, there are some technical difficulties caused by $\lambda<0$ to be overcome. In addition, an extra assumption called as the mixed version of the reverse H\"{o}lder class be required in the proof of the converse characterization. Moreover, some further interesting conclusions for the Hardy type operators on mixed $\lambda$-central Morrey space $\mathcal{B}^{\vec{p},\lambda}(\mathbb{R}^{n})$ are also derived.

math.FA↗

arXiv2022

Fractional integral operators on the mixed $\lambda$-central central Morrey spaces

In this paper, the authors define the mixed $\lambda$-central Morrey spaces and the mixed $\lambda$-central $BMO$ spaces. The boundedness of the fractional integral operators $T_{\alpha}$ and its commutators $[b, T_{\alpha}]$ are established on the mixed $\lambda$-central Morrey spaces, respectively. Furthermore, we also extend these results to the generalized mixed central Morrey spaces.

math.FA↗

arXiv2022

Boundedness of intrinsic square functions and commutators on generalized central Morrey spaces

In this paper, the authors establish the boundedness for a large class of intrinsic square functions $\mathcal{G}_{\alpha}$, $g_{\alpha}$, $g^{\ast}_{\tilde{\lambda},\alpha}$ and their commutators $[b,\mathcal{G}_{\alpha}]$, $[b,g_{\alpha}]$ and $[b,g^{\ast}_{\tilde{\lambda},\alpha}]$ generated with $\lambda$-central $BMO$ functions $b\in CBMO^{p,\lambda}(\mathbb{R}^{n})$ on generalized central Morrey spaces $\mathcal{B}^{q,\varphi}(\mathbb{R}^{n})$ for $1<q<\infty,0<\alpha\leq1$, respectively. All of the results are new even on the central Morrey spaces $\mathcal{B}^{q,\lambda}(\mathbb{R}^{n})$.

math.FA↗