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A Note on Potentials of Imaginary Order in Variable Generalized Holomorphic Hölder Spaces
AbstractIn this note we study a generalization of a holomorphic Bergman-type projection, namely, the operator of fractional integro-differentiation...
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Toeplitz operators on the space of all holomorphic functions on finitely connected domains
We define and study Toeplitz operators on the Fréchet space of all holomorphic functions on finitely connected domains in the Riemann sphere. We...
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Variable order fractional integrals in variable generalized Hölder spaces of holomorphic functions
We introduce and study the variable generalized Hölder spaces of holomorphic functions over the unit disc in the complex plane. These spaces are...
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The Nonlinear Boundary Value Problem for k Holomorphic Functions in ℂ2
k holomorphic functions are a type of generation of holomorphic functions. In this paper, a nonlinear boundary value problem for k holomorphic...
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Proper Holomorphic Map**s
In this chapter we extend the results of the previous chapters to proper holomorphic map**s. For this we introduce proper holomorphic...
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Continuous Extension of Holomorphic Map**s
In this chapter introduce the Kobayashi-Royden and other invariant metrics, and prove continuous extension to the boundary of proper holomorphic maps...
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Holomorphic Correspondences
In this chapter we prove that if a proper holomorphic map between bounded domains in...
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Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces
The paper is devoted to weighted estimates for operators of fractional integration of variable order of Bergman type in generalized variable Hölder...
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Boundary Smoothness of Holomorphic Map**s
In this chapter we prove, using the scaling method, smooth extension to the boundary of biholomorphic maps between strictly pseudoconvex domains
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Cauchy singular integral operator with parameters in Log-Hölder spaces
This paper is motivated by a claim in the classical textbook of Muskhelishvili concerning the Cauchy singular integral operator S on Hölder functions...
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Hölder continuity for solutions of the complex Hessian type equation
In this paper we prove the Hölder continuity for the Hessian equation on a m -hyperconvex domain of m -subharmonic type k . As an application we prove...
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H2-Norms of Partial Sums of the Fourier Series in the Laguerre Basis for Bounded Holomorphic Functions
We compute the upper bounds for the H 2 -norms of partial sums of the Fourier series in the Laguerre basis on the unit ball in the space of bounded...
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Bianalytic functions of Hölder classes in Jordan domains with nonanalytic boundaries
We consider some boundary behavior effect for bianalytic functions related to the Dirichlet problem solvability. It is proved that there exist such...
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Two Coefficient Conjectures for Nonvanishing Hardy Functions, I
There are two eminent still open conjectures for nonvanishing holomorphic Hardy functions f(z) on the unit disk. The Hummel–Scheinberg–Zalcman...
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Holomorphic solutions and solvability theory for a class of linear complete singular integro-differential equations with convolution by Riemann–Hilbert method
In this article, we investigate a class of linear complete singular integro-differential equations of convolution type with Fredholm integral...