Related papers: On harmonic functions and the Schwarz lemma

Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…

For a bounded domain equipped with a piecewise Lipschitz continuous Riemannian metric g, we consider harmonic map from $(\Omega, g)$ to a compact Riemannian manifold $(N,h)\subset\mathbb R^k$ without boundary. We generalize the notion of…

This article examines a family of smooth mappings between Banach spaces and establishes conditions for the existence of their zeros. Applications to fixed-point problems and the Implicit Function Theorem are also discussed.

We consider the class univalent log-harmonic mappings on the unit disk. Firstly, we obtain necessary and sufficient conditions for a complex-valued continuous function to be starlike or convex in the unit disk. Then we present a general…

In this work we derive a functional equation in terms of the Hurwitz-Lerch zeta function along with definite integrals in terms of the incomplete gamma and Hurwitz-Lerch zeta functions. The method used in these derivations is contour…

This paper is devoted to the investigation of multidimensional analogues of refined Bohr-type inequalities for bounded holomorphic mappings on the unit polydisc $\mathbb{P}\Delta(0;1_n)$. We provide a definitive resolution to the Bohr…

The mean flux theorems are proved for solutions of the Helmholtz equation and its modified version. Also, their converses are considered along with some other properties which generalise those that guarantee harmonicity.

We give a local characterization of the class of functions having positive distributional derivative with respect to $\bar{z}$ that are almost everywhere equal to one of finitely many analytic functions and satisfy some mild non-degeneracy…

In this note, we consider certain logharmonic mappings in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}.$ Next, we obtain sharp bound of pre-Schwarzian norm of such logharmonic mappings in the unit disk. Then we discuss growth theorem…

Our concern in this paper is to study the qualitative properties for harmonic functions related to the fractional Laplacian. Firstly we classify the polynomials in the whole space and in the half space for the fractional Laplacian defined…

We study a cut-off function lemma in projective spaces. We believe that this is well-known. We provide the details of the computation for later uses.

In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of $L$-series of harmonic Maass forms to state and prove a summation formula for such…

In this paper, we first establish a Schwarz-Pick type theorem for pluriharmonic mappings and then we apply it to discuss the equivalent norms on Lipschitz-type spaces. Finally, we obtain several Landau's and Bloch's type theorems for…

We prove some properties of completely monotonic functions and apply them to obtain results on gamma and $q$-gamma functions.

We propose an affine version of the Schwarz map for the hypergeometric differential equation, and study its image when the monodromy group is finite.

In this paper, we prove some splitting results for manifolds supporting a non-constant infinity harmonic function which has at most linear growth on one side. Manifolds with non-negative Ricci or sectional curvature are considered. In…

We discuss a class of regions and conformal mappings which are useful in several problems of approximation theory, harmonic analysis and spectral theory.

This paper is devoted to the investigation of harmonic and biharmonic functions on vector bundles equipped with spherically symmetric metrics. We will study the biharmonicity of vertical lifts of functions as well as $r$-radial functions on…

With an easy application of maximum principle, we establish a Schwarz-type lemma for squeezing function on finitely connected planar domains that directly yields the explicit formula for squeezing function on doubly connected domains…

In this paper, we investigate the relationships between linear measure and harmonic mappings.