Peyo Stoilov
The present note contains a generalization of a theorem of Hallenbeck and Samotij for the multipliers of Cauchy integrals of logarithmic potentials.
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In this paper we prove some interpolation theorems for the multipliers of the Cauchy- Stiltjes type integrals
The present paper contains a generalization of some interpolation theorems of S. A. Vinogradov.
Special classes of analytic functions, denoting by K and J arc considered in this paper.
In this article, we first establish an $L^2$-type Dolbeault isomorphism for the sheaf of logarithmic differential forms twisted by the multiplier ideal sheaf. By using this isomorphism and $L^2$-estimates equipped with a singular Hermitian metric, we obtain logarithmic vanishing theorems involving multiplier ideal sheaves on compact Kähler manifolds with simple normal crossing divisors.
Logarithmic Bloch spaces in the polydisc, endpoint results for Hankel operators and pointwise multipliers
本文研究单位多圆盘中的两类对数 Bloch 空间，利用有界 Hankel 算子的符号给出等价刻画，并完整描述不同 Bloch 空间之间的逐点乘子。
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} {…
Integrals of logarithmic forms on semi-algebraic sets and a generalized Cauchy formula Part II: generalized Cauchy formula
本文作为系列论文第二部分，证明了射影直线乘积上对数形式积分的广义柯西公式，并将其应用于混合泰特动机的霍奇实现构造。
Estimates of the modulus of continuity of the logarithmic double layer potential in the closure of domain
本文基于Ahlfors正则积分曲线边界域，对Cauchy型积分实部的模连续性进行更精确的估计，通过构造例子验证估计的准确性。
In this paper consisting of two parts, we study the integral of a logarithmic differential form on a compact semi-algebraic set in R^n or C^n. In Part I, we prove the convergence of the integral when the semi-algebraic set satisfies allowability (or admissibility), a condition on the dimension of the intersection of the set and the pole divisor of the differential form.
A new proof of the inequalities of D. J. Hallenbeck for the Area functions of multipliers of fractional Cauchy transforms is given.
The continuous extension of the logarithmic double layer potential to the Ahlfors-regular boundary
本文研究Cauchy型积分实部（即双层对数位势）的边界行为，给出了其到Ahlfors-正则边界连续延拓的充要条件。
We investigate differentiability of functions defined on regions of the real quaternion field and obtain a noncommutative version of the Cauchy-Riemann conditions. Then we study the noncommutative analog of the Cauchy integral as well as criteria for functions of a quaternion variable to be analytic. In particular, the quaternionic exponential and logarithmic functions are being considered. Main results include quaternion versions of Hurwitz' theorem, Mittag-Leffler's theorem and Weierstrass theorem.
In this article, we present that for any complex manifold whose dimension is bigger than one, there exists a multiplier ideal sheaf such that there don't exist equisingular weights with logarithmic poles, which are not smaller than the orginal weight. A direct consequence is the nonexistence of decreasing equisingular approximations with logarithmic poles.
In the paper, the authors show that the weighted geometric mean and the logarithmic mean are Bernstein functions and establish integral representations of these means by Cauchy's integral theorem in the theory of complex functions.
The classical Enestrom-Kakeya theorem establishes upper and lower bounds on the zeros of a polynomial with positive coefficients that are explicit functions of those coefficients. We establish a unifying framework that incorporates this theorem and several similar ones as special cases, while generating new theorems of a similar type. These establish zero inclusion and exclusion regions consisting of a single disk or the union of several disks in the complex plane. Our framework is built on two basic tools, namely a generalization of an observation by Cauchy, and a family of polynomial multipl…
The Cauchy problem for the homogeneous (real and complex) Monge-Ampere equation (HRMA/HCMA) arises from the initial value problem for geodesics in the space of Kahler metrics. It is an ill-posed problem. We conjecture that, in its lifespan, the solution can be obtained by Toeplitz quantizing the Hamiltonian flow defined by the Cauchy data, analytically continuing the quantization, and then taking a kind of logarithmic classical limit. In this article, we prove that in the case of torus invariant metrics (where the HCMA reduces to the HRMA) this "quantum analytic continuation potential" coincid…
Weighted equilibrium in a field of a uniform charge of an interval
研究区间[-1,1]上均匀背景电荷产生的外部场下的对数平衡问题，确定不同τ值下的平衡测度、支持集及平衡常数，揭示支持集拓扑结构和密度随τ变化的演变。
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