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Jianjun Jin

Publications and source records attributed to Jianjun Jin.

16 recordsLinked to original sources
arXiv2026

$l^{p}-L^{q}$ boundedness of sequence-to-function Hardy-Littlewood-P\'{o}lya-type operators

In this paper we deal with the boundedness of certain generalized sequence-to-function Hardy-Littlewood-P\'{o}lya-type operators. We completely characterize the $l^{p}-L^{q}$ boundedness of these operators for all $(p, q)\in [1, \infty]\times[1, \infty]$. These results complement some previous results in the literature. Our method relies on the ideas of generalized Schur's tests developed by Okikiolu, Sinnamon, Tao and Zhao.

math.CA↗
arXiv2026

Sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function

In this note we study the multiplier norm estimates for the multiplication operators between weighted Bergman spaces, whose symbols are the higher-order Schwarzian derivatives of univalent functions. We establish sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function. This extends a related result by Shimorin. The proof of our new theorem relies on an explicit formula for the higher-order Schwarzian derivatives of the Koebe function and a recent theorem from our earlier work. We finally point out that the Koebe function is still the extremal function for certain higher-order Schwarzians of the univalent functions.

math.CV↗
arXiv2026

On the norms of the multiplication operators between weighted Bergman spaces

In this paper, we study the norms of multiplication operators acting between weighted Bergman spaces. First, we provide a proof for a norm estimate previously announced in our recent paper \cite{Jin-c}. Second, we establish a sharp norm estimate for certain special multiplication operators between weighted Bergman spaces, a result that is novel to the literature. Finally, we also discuss the connections between the Brennan conjecture and related multiplier norms induced by the Schwarzian derivative of univalent functions.

math.FA↗
arXiv2025

Complex exponential integral means spectra of univalent functions and the Brennan conjecture

In this paper we investigate the complex exponential integral means spectra of univalent functions in the unit disk. We show that all integral means spectrum (IMS) functionals for complex exponents on the universal Teichm\"uller space, the closure of the universal Teichm\"uller curve, and the universal asymptotic Teichm\"uller space are continuous. We also show that the complex exponential integral means spectrum of any univalent function admitting a quasiconformal extension to the extended complex plane is strictly less than the universal integral means spectrum. These extend some related results in our recent work \cite{Jin}. Here we employ a different and more direct approach to prove the continuity of the IMS functional on the universal asymptotic Teichm\"uller space. Additionally, we completely determine the integral means spectra of all univalent rational functions in the unit disk. As a consequence, we show that the Brennan conjecture is true for this class of univalent functions. Finally, we present some remarks and raise some problems and conjectures regarding IMS functionals on Teichm\"uller spaces, univalent rational functions, and a multiplication operator whose norm is closely related to the Brennan conjecture.

math.CV↗
arXiv2025

On the discrete Hilbert-type operators

Recently, Bansah and Sehba studied in [3] the boundedness of a family of Hilbert-type integral operators, where they characterized the $L^{p}-L^{q}$ boundedness of the operators for $1\leq p\leq q\leq \infty$. In this paper, we deal with the corresponding discrete Hilbert-type operators acting on the weighted sequence spaces. We establish some sufficient and necessary conditions for the $l^{p}-l^{q}$ boundedness of the operators for $1\leq p\leq q\leq \infty$. We find out that the conditions of the boundedness of discrete Hilbert-type operators are different from those of the boundedness of Hilbert-type integral operators. Also, for some special cases, we obtain sharp norm estimates for discrete Hilbert-type operators. Finally, it is pointed out that certain extensions of the theorems given in [3] can be established by using our different arguments.

math.FA↗
arXiv2025

Boundedness and norm of certain p-adic Hardy-Littlewood-P\'{o}lya-type operators

In this paper, by introducing some parameters, we define and study certain $p$-adic Hardy-Littlewood-P\'{o}lya-type integral operators acting on $p$-adic weighted Lebesgue spaces. We completely characterize $L^{q}-L^{r}$ boundedness of these operators for all $(q, r)\in [1, \infty]\times[1, \infty]$. For some special cases, we obtain sharp norm estimates for the operators. These results are not only a complement to some previous results but also an extension of existing ones in the literature.

math.FA↗
arXiv2025

Generalized Hilbert matrix operators acting on weighted sequence spaces

In this paper we introduce and study a new kind of generalized Hilbert matrix operators, induced by a positive finite Borel measure on (0,1), acting on weighted sequence spaces. We establish a sufficient and necessary condition for the boundedness of these operators. These results extend some related ones obtained recently in [Bull. London Math. Soc., 55 (2023), no. 6, 2598-2610].

math.CA↗
arXiv2024

Integral means spectrum functionals on Teichmuller spaces

In this paper we introduce and study the integral means spectrum (IMS) functionals on Teichm\"uller spaces. We show that the IMS functionals on the closure of the universal Teichm\"uller space and the universal asymptotic Teichm\"uller space are both continuous. During the proof, we consider the Pre-Schwarzian derivative model of universal asymptotic Teichm\"uller space and establish some new results for it. We also show that the integral means spectrum of any univalent function admitting a quasiconformal extension to the extended complex plane is strictly less than the universal integral means spectrum.

math.CV↗
arXiv2023

Prawitz's area theorem and the mixed Aharonov sequence

In this paper, motivated by the Prawitz area theorem and the work of Aharonov, we introduce the mixed Aharonov sequence associated with a locally univalent analytic function. By using the mixed Aharonov sequence, we establish a new univalence criterion for the locally univalent analytic functions in the unit disk, which generalizes some related results of Aharonov in \cite{Ah}. We also prove some new properties about the (mixed) Aharonov sequence, in particular, a new inequality for the Aharonov sequence is established for the univalent functions with a quasiconformal extension.

math.CV↗
arXiv2022

On a multiplier operator induced by the Schwarzian derivative of univalent functions

In this paper we study a multiplier operator which is induced by the Schwarzian derivative of univalent functions with a quasiconformal extension to the extended complex plane. As applications, we show that the Brennan conjecture is satisfied for a large class of quasidisks. We also establish a new characterization of asymptotically conformal curves and of the Weil-Petersson curves in terms of the multiplier operator.

math.CV↗
arXiv2022

Hilbert-type operators acting between weighted Fock spaces

In this paper we introduce and study several new Hilbert-type operators acting between the weighted Fock spaces. We provide some sufficient and necessary conditions for the boundedness and compactness of certain Hilbert-type operators from one weighted Fock space to another.

math.FA↗
arXiv2022

On the Hilbert-type operators acting from function spaces into sequence spaces

In this paper we introduce and study some Hilbert-type operators acting from the function spaces into the sequence spaces. We give some sufficient and necessary conditions for the boundedness and compactness of these Hilbert-type operators. Also, for some special cases, we obtain the sharp estimates for the norms of certain Hilbert-type operators.

math.FA↗
arXiv2022

On the operators of Hardy-Littlewood-P\'olya type

In this paper we introduce and study several new Hardy-Littlewood-P\'olya-type operators. In particular, we study a Hardy-Littlewood-P\'olya-type operator induced by a positive Borel measure on $[0,1)$. We establish some sufficient and necessary conditions for the boundedness (compactness) of these operators. We also determine the exact values of the norms of the Hardy-Littlewood-P\'olya-type operators for certain special cases.

math.FA↗
arXiv2021

Generalized Cesàro operators on Dirichlet-type spaces

In this note, we introduce and study a new kind of generalized Cesàro operators $\mathcal{C}_μ$, induced by a positive Borel measure $μ$ on $[0, 1)$, between the Dirichlet-type spaces. We characterize the measures $μ$ for which $\mathcal{C}_μ$ is bounded (compact) from one Dirichlet-type space $\mathcal{D}_α$ into another one $\mathcal{D}_β$.

math.CA↗
arXiv2021

Generalized Hilbert series operators

In this note we study the generalized Hilbert series operator $H_μ$, induced by a positive Bore measure $μ$ on $[0, 1)$, between weighted sequence spaces. We characterize the measures $μ$ for which $H_μ$ is bounded between different sequence spaces. Finally, for certain special measures, we obtain the sharp norm estimates of the operators and establish some new generalized Hilbert series inequalities with the best constant factors.

math.CA↗