This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers acting on M${\rm \ddot{o}}$bius invariant spaces $Q_p$, which unify BMOA and Bloch space in the scale of $p$. The boundedness and compactness of these operators on $Q_p$ spaces are determined by means of an embedding theorem, i.e. $Q_p$ spaces boundedly embedded in the non-isotropic tent type spaces $T_q^\infty$.

2011-09-08math.CVmath.FA

The Stieltjes integrals in the theory of harmonic and analytic functions

We study various Stieltjes integrals as Poisson-Stieltjes, conjugate Poisson-Stieltjes, Schwartz-Stieltjes and Cauchy-Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the singular Hilbert-Stieltjes integral in the sense of the principal value. These results hold for arbitrary $2π-$periodic bounded integrands that are differentiable a.e. and, in particular, for integrands of the class ${\cal {CBV}}$ (countably bounded variation).

2019-09-23math.CV

On some interpolation theorems for the multipliers of the Cauchy- Stiltjes type integrals

In this paper we prove some interpolation theorems for the multipliers of the Cauchy- Stiltjes type integrals

2008-08-06math.CV

Note on the multipliers of Cauchy integrals of logarithmic potentials

The present note contains a generalization of a theorem of Hallenbeck and Samotij for the multipliers of Cauchy integrals of logarithmic potentials.

2008-07-28math.CV

Free interpolation of families of Cauchy-Stiltjes integrals and their multipliers

The present paper contains a generalization of some interpolation theorems of S. A. Vinogradov.

2008-07-23math.CV

Multipliers of integrals of Cauchy - Stieltjes type

Let ${\rm {\mathbb G}}$ be a domain with closed rectifiable Jordan curve $\ell $ . Let $K({\rm {\mathbb G}})$ be the space of all analytic functions in ${\rm {\mathbb G}} $ representable by a Cauchy - Stieltjes integral. Let ${\rm {\mathfrak M}}(K)$ be the class of all multipliers of the space $K({\rm {\mathbb G}}).$ In this paper we prove that if $f$ is bounded analytic function on ${\rm {\mathbb G}}$ and $${\kern 1pt} {\kern 1pt} {\kern 1pt} \mathop{ess\sup}\limits_{η\in \ell } \int_{\ell} \frac{|f(ζ)-f(η)|}{|ζ-η|} |dζ|{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {…

2009-01-13math.CVmath.FA

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University of Helsinki（赫尔辛基大学）

本文利用变量非依赖性质和对称公式，推导了多变量Herglotz-Nevanlinna函数对称延拓的解析刻画，并扩展了Cauchy型函数的Stieltjes反演公式。

2021-02-16math.CV

Note on the growth of Area functions

A new proof of the inequalities of D. J. Hallenbeck for the Area functions of multipliers of fractional Cauchy transforms is given.

2008-07-24math.CV

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Central limit measure for V-monotone independence

该文研究V-单调独立性的中心极限分布，通过Cauchy–Stieltjes变换证明其关于Lebesgue测度绝对连续、给出密度隐式形式并附计算机生成的密度图像。

2023-07-20math.CVmath.FAmath.PR

Noncommutative complex analysis and Bargmann-Segal multipliers

We state several equivalent noncommutative versions of the Cauchy-Riemann equations and characterize the unbounded operators on L^2(R) which satisfy them. These operators arise from the creation operator via a functional calculus involving a class of entire functions, identified by Newman and Shapiro [D. J. Newman and H. S. Shapiro, Fischer spaces of entire functions, in Entire Functions and Related Parts of Analysis (J. Koorevaar, ed.), AMS Proc. Symp. Pure Math. XI (1968), 360-369], which act as unbounded multiplication operators on Bargmann-Segal space.

1999-08-06math.CVmath.OA

Regularized Limit, analytic continuation and finite-part integration

Finite-part integration is a recent method of evaluating a convergent integral in terms of the finite-parts of divergent integrals deliberately induced from the convergent integral itself [E. A. Galapon, Proc. R. Soc., A 473, 20160567 (2017)]. Within the context of finite-part integration of the Stieltjes transform of functions with logarithmic growths at the origin, the relationship is established between the analytic continuation of the Mellin transform and the finite-part of the resulting divergent integral when the Mellin integral is extended beyond its strip of analyticity. It is settled …

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海森堡群上的旗Hardy空间理论及其应用

Flag Hardy space theory on Heisenberg groups and applications

本文在海森堡群上建立了完整的旗Hardy空间理论，通过原子分解和多种函数给出刻画，引入新技术克服非交换性等困难，并应用于证明奇异积分算子有界性等结论。

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Convergence of random holomorphic functions with real zeros and extensions of the stochastic zeta function

本文建立收敛点过程到零点由其确定的随机全纯函数泛函收敛的统一框架，推广随机矩阵特征多项式与随机 zeta 函数结果，并证明极限点过程的 Stieltjes 变换几乎处处服从标准 Cauchy 分布。

2024-10-26math.CVmath.NTmath.PR