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Schwarz–Pick Estimates of the Real Unit Ball for Harmonic Map**s
In this paper, Schwarz–Pick estimates are obtained for harmonic map**s from the unit ball of ℝ n into origin-symmetric bounded convex domains Ω ⊂ ℝ m ,...
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Carleson measures for weighted harmonic mixed norm spaces on bounded domains in ℝn
We study weighted mixed norm spaces of harmonic functions defined on smoothly bounded domains in ℝ n . Our principal result is a characterization of...
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Boundary behavior of harmonic functions on metric measure spaces with non-negative Ricci curvature
Let ( X, d, μ ) be a metric measure space with non-negative Ricci curvature. This paper is concerned with the boundary behavior of harmonic function on...
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Stability of elliptic Harnack inequalities
We survey some recent progress in the study of stability of elliptic Harnack inequalities under form-bounded perturbations for strongly local...
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Khavinson Problem for Hyperbolic Harmonic Map**s in Hardy Space
In this paper, we partly solve the generalized Khavinson conjecture in the setting of hyperbolic harmonic map**s in Hardy space. Assume that
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Volume Growth and On-diagonal Heat Kernel Bounds on Riemannian Manifolds with an End
We investigate heat kernel estimates of the form p t ( x , x ) ≥ c x t − α , for large enough t , where α and c x are positive reals and c x may depend on x , on...
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A Schwarz Lemma for Harmonic Functions in the Real Unit Ball
We establish a precise Schwarz lemma for real-valued and bounded harmonic functions in the real unit ball of dimension n . This extends Chen’s...
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Arsove–Huber Theorem in Higher Dimensions
In this note we briefly present the progress in the research project to extend Huber’s theory of surfaces to general dimensions. The full paper [42]...
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Three-dimensional electric potential induced by a point singularity in a multilayered dielectric medium
A simple and effective method is proposed to derive the three-dimensional electric potential induced by a point singularity of any type in an N -phase...
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Non-absolutely Convergent Generalized Laplacian
For possibly discontinuous functions including, for instance, Sobolev functions, we present new Blaschke-Privaloff-type criteria for superharmonicity...
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Zero extension for Poisson’s equation
In this paper, we present a necessary and sufficient condition to guarantee that the extended function of the solution for Poisson’s equation in a...
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Quantitative Absolute Continuity of Harmonic Measure and the Dirichlet Problem: A Survey of Recent Progress
It is a well-known folklore result that quantitative, scale invariant absolute continuity (more precisely, the weak- A ∞ property) of harmonic measure...
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On the Maximum Principle for the Riesz Transform
Let μ be a measure in ℝd with compact support and continuous density, and let Rsμ(x) = | y – x |y – x|s+1 dμ(y), x,y∈ ℝd, 0 < s < d. We consider the...