arXiv subjects

Zixing Yuan

Publications and source records attributed to Zixing Yuan.

5 recordsLinked to original sources

arXiv2026

Volterra operators on the BMOA space of Dirichlet series

In this paper, we completely characterize the boundedness and compactness of Volterra operators on $BMOA_{\mathcal D}$, the BMOA space of Dirichlet series, and estimate their essential and weak essential norms. We further prove that compactness, weak compactness, and complete continuity are equivalent for these operators. In particular, every Dirichlet polynomial symbol induces a compact Volterra operator on $BMOA_{\mathcal D}$. We also prove that every such symbol induces a compact Volterra operator on the Bergman space of Dirichlet series $\mathcal A_μ^1$ for every admissible measure $μ$, extending the corresponding compactness theorem, previously established for $1<p<\infty$, to the endpoint $p=1$.

math.FA↗

arXiv2026

Area operators on Hardy spaces of Dirichlet series II: counterexamples and compactness criteria

We study area operators $\mathbb{A}_{μ,l}$, $0<l<\infty$, induced by positive Borel measures on the right half-plane and acting on the Hardy spaces of Dirichlet series $\mathscr H^p$, $0<p<\infty$. We first disprove a conjecture proposed by the present authors in an earlier work by constructing a probability measure, valid for all $0<p,l<\infty$, for which the associated area operator is bounded although the measure fails the proposed Carleson conditions. We then characterize the boundedness and compactness of $\mathbb{A}_{μ,l}$ on both $\mathscr H^p$ and the Hardy space $\mathscr H^p_0$ of Dirichlet series vanishing at $+\infty$, for every $0<p,l<\infty$, via integrability conditions for the associated cone integrals. In particular, the boundedness and compactness are equivalent for these operators. We also give direct proofs of compactness under vanishing Carleson measure and compact $H_{\mathrm i}^p$-Carleson embedding hypotheses. As an application, we establish an estimate for the essential norms of bounded Volterra operators. This leads to a complete characterization of compactness for Volterra operators on $\mathscr{H}^p$ and provides a different proof of compactness for those with Dirichlet series symbols in $\operatorname{VMOA}(\mathbb C_0)$.

math.FA↗

arXiv2026

Cesàro-type operators on average radial integrability spaces induced by doubling weights

In this paper, we study the Cesàro-type operator $$ \Ces_{μ,β}f(z)=\int_{[0,1)}\frac{f(tz)}{(1-tz)^β}\,dμ(t), $$ where $μ$ is a positive Borel measure on $[0,1)$ and $β>0$. For $0<p,q<\infty$ and radial doubling weights $ω_1,ω_2$, we prove that $\Ces_{μ,β}:\AL_p^q(ω_1)\to\AL_p^q(ω_2)$ is bounded if and only if $$ μ([0,1))+\sup_{1/2\le r<1}\frac{μ([r,1))}{(1-r)^β}\left(\frac{\whatω_2(r)}{\whatω_1(r)}\right)^{1/p}<\infty, $$ and its norm is comparable to this quantity. For standard weights, our result extends \cite{BlascoMas2026,GalanopoulosSiskakisZhao2025} to the full range $0<p=q<\infty$. We further characterize compactness and the essential norm on average radial integrability spaces induced by doubling weights.

math.FA↗

arXiv2026

Metrically bounded Volterra-type operators on area Nevanlinna spaces

In this paper, we study metrically bounded Volterra-type operators $J_g$ and $I_g$ on the area Nevanlinna spaces $N_α^p$, where $1\le p<\infty$ and $α>-1$. Choe, Koo and Smith \cite{CKS} obtained partial characterizations of the corresponding symbol classes, but the exact characterization was still open. We establish a Littlewood--Paley type characterization of $N_α^p$ and use it to resolve this problem affirmatively. More precisely, $J_g$ is metrically bounded on $N_α^p$ if and only if $g$ belongs to the Bloch space $\mathcal B$, while $I_g$ is metrically bounded on $N_α^p$ if and only if $g\in H^\infty$.

math.FA↗

arXiv2025

Embedding derivatives and derivative Area operators of Hardy spaces into Lebesgue spaces

We characterize the compactness of embedding derivatives from Hardy space $H^p$ into Lebesgue space $L^q(μ)$. We also completely characterize the boundedness and compactness of derivative area operators from $H^p$ into $L^q(\mathbb{S}_n)$, $0<p, q<\infty$. Some of the tools used in the proof of the one-dimensional case are not available in higher dimensions, such as the strong factorization of Hardy spaces. Therefore, we need the theory of tent spaces which was established by Coifman, Mayer and Stein in 1985.

cs.IR↗