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We establish plurisubharmonicity of envelopes of certain classical disc functionals on locally irreducible complex spaces, thereby generalizing the corresponding results for complex manifolds. We also find new formulae expressing the…
Recent progress in analytical calculation of the multiple [inverse, binomial, harmonic] sums, related with epsilon-expansion of the hypergeometric function of one variable are discussed.
The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions $f$ on the unit ball $B_E$ of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch…
Using results from theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essential tools are the theory of unitary dilation of a contraction…
In a seminal paper, Choquet introduced an integral formula to extend a monotone increasing setfunction on a sigma-algebra to a (nonlinear) functional on bounded measurable functions. The most important special case is when the setfunction…
A basic result in the theory of holomorphic functions of several complex variables is the following special case of the work of H. Cartan on the sheaf cohomology on Stein domains ([10], or see [14] or [16] for more modern treatments).
In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to…
Generalized Lelong numbers of plurisubharmonic functions with respect to plurisubharmonic weights (due to Demailly) are specified for weights with multicircled asymptotics. Explicit formulas for these values are obtained in terms of the…
In this work we establish a connection between two classical notions, unrelated so far: Harmonic functions on the one hand and absolutely monotonic functions on the other hand. We use this to prove convexity type and propagation of…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
Additional integral inequalities are obtained for integrals of the differences of subharmonic functions by Borel measures on balls in a multidimensional Euclidean space. These integrals are still estimated from above through the Nevanlinna…
In this paper, we show that the extremal length functions on Teichm\"uller space are log-plurisubharmonic. As a corollary, we obtain an alternative proof of L.Liu and W.Su's results on the plurisubharmonicity of extremal length functions.…
In a setting, where only exit measures are given, as they are associated with a right continuous strong Markov process on a separable metric space, we provide simple criteria for scaling invariant H\"older continuity of bounded harmonic…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
We establish the equivalence between superharmonic functions and locally renormalized solutions for the elliptic measure data problems with $(p, q)$-growth. By showing that locally renormalized solutions are essentially bounded below and…
In this note it is shown that two key results on transcendental singularities for meromorphic functions of finite lower order have refinements which hold under the weaker hypothesis that the logarithmic derivative has finite lower order.
Let G be a connected, real, semisimple Lie group contained in its complexification G_C, and let K be a maximal compact subgroup of G. We construct a K_C-G double coset domain in G_C, and we show that the action of G on the K-finite vectors…
In this paper we deal with improvement of Jensen, Jensen-Steffensen's and Jensen's functionals related inequalities for uniformly convex, phi-convex and superquadratic functions.
The Whittaker function and its diverse extensions have been actively investigated. Here we introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function $\Phi_{p,v}$ and investigate some of…
We present a modified version of the Arakelyan's result: a relationship between holomorphic extension of a holomorphic function on the unit disc onto the domain $\mathbb C\setminus[1,\infty)$ and its Taylor coefficients' interpolation.