arXiv subjects

Zhaopeng Lin

Publications and source records attributed to Zhaopeng Lin.

5 recordsLinked to original sources

arXiv2026

Corona theorem for the quaternionic Hardy space

The finite-generator corona theorem for bounded slice regular functions on the quaternionic unit ball was recently established by Colombo, Pozzi, Sabadini, and Wick. In the present paper, we extend the quaternionic $H^\infty$-corona theorem to countably many generators and obtain quantitative estimates that are independent of the cardinality of the generating family. We also establish the corresponding $H^p$-corona theorem for the full range $1\leq p<\infty$, with quantitative norm estimates for both finite and countable families of generators. In the Hilbert-space setting, we prove a quaternionic Leech factorization theorem for Hardy-space multipliers and derive, as a consequence, a Toeplitz corona characterization. Our approach is based on a fixed-slice $2\times2$ complex matrix realization of the slice regular product, together with operator-valued corona and factorization techniques.

math.FA↗

arXiv2026

Isometric Composition Operators on $BMOA$ for $0<p<\infty$

We characterize the analytic self-maps of the unit disk inducing isometric composition operators on $\BMOA$ with respect to the M\"obius-invariant $H^p$ norm for $p\ge1$ and the corresponding quasi-norm for $0<p<1$. In particular, this gives a complete answer to Laitila's question on the characterization of isometric composition operators for the M\"obius-invariant $H^p$ norms, while also covering the quasi-Banach range. As a consequence, the isometric property of $C_\varphi$ is independent of the exponent $p\in(0,\infty)$.

math.FA↗

arXiv2026

A Fourier Criterion for the Toeplitzness of Operators on Fock Spaces

We give a Fourier criterion for the Toeplitzness of bounded operators on Fock spaces, where Toeplitzness means representability as a Toeplitz operator with a bounded measurable symbol. For a Toeplitz operator, the anti-diagonal restriction of its canonical kernel is the Fourier transform of the Gaussian-weighted symbol. Consequently, Fourier inversion of this anti-diagonal restriction recovers the unique bounded symbol whenever such a representation exists. As applications, we characterize the Toeplitzness of weighted composition operators and generalized Volterra-type operators.

math.FA↗

arXiv2026

Slice Regular Composition Operators on Quaternionic Fock Spaces via Matrix Realization

We characterize the boundedness and compactness of slice regular composition operators between quaternionic Fock spaces for the full range $0<p,q<\infty$, without assuming that the composition symbol preserves a fixed complex slice. As applications of the same method, we also obtain corresponding criteria for weighted composition operators and for products of Volterra-type integral operators with slice regular composition operators. The main tool is a fixed-slice matrix realization of the regular product, which represents slice regular composition on a fixed complex slice through a holomorphic $2\times 2$ matrix functional calculus. This representation reveals a genuinely quaternionic rigidity phenomenon: boundedness imposes affine restrictions on the eigenvalue functions of the associated matrix symbol rather than on the original symbol itself. In particular, the original symbol need not be affine, and affine eigenvalue functions alone do not characterize boundedness.

math.FA↗

arXiv2026

Toeplitz Operators on Quaternionic Fock Spaces

We characterize boundedness and compactness of Toeplitz operators on quaternionic Fock spaces with positive measure symbols and slice-function symbols in $\mathrm{BMO}^1$. For positive measure symbols, we derive criteria using normalized reproducing kernels and symmetric box averages, while for slice $\mathrm{BMO}^1$ symbols, the characterizations rely on the Berezin transform. We further introduce a global quaternionic Fock space $F_\alpha^p$ to define Toeplitz operators with real-valued measure symbols; this space is built by integrating slice regular functions over all complex slices of $\mathbb{H}$ and is norm-equivalent to the standard slice-based quaternionic Fock space. In the Hilbert space case $p=2$, a slice-independent orthogonal projection exists, which allows us to define Toeplitz operators with real-valued measure symbols and slice-function symbols in a unified way.

math.FA↗