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Mean value properties of harmonic functions on Sierpinski gasket type fractals
Sierpinski gasket Laplacian harmonic function mean value property analysis on fractals
2012/6/27
In this paper, we establish an analogue of the classical mean value property for both the harmonic functions and some general functions in the domain of the Laplacian on the Sierpinski gasket. Further...
Radius of Close-to-convexity of Harmonic Functions
Coefficient inequality partial sums radius of univalence analytic univalent convex and starlike harmonic functions
2011/8/24
Abstract: Let ${\mathcal H}$ denote the class of all normalized complex-valued harmonic functions $f=h+\bar{g}$ in the unit disk ${\mathbb D}$, and let $K=H+\bar{G}$ denote the harmonic Koebe function...
On some extremal problems in spaces of harmonic functions
Bergman spaces distance estimates extremal problems harmonic functions
2011/9/19
Abstract: We give solutions to some extremal problems involving distance function in mixed norm spaces of harmonic functions on the unit ball of R^n.
Singular integrals on self-similar sets and removability for Lipschitz harmonic functions in Heisenberg groups
Singular integrals self-similar sets removability Heisenberg group
2011/1/20
In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean space...
It is proved that the fundamental group of the space of harmonic polynomials of degree n(n ≥ 2), with the same Gaussian curvature is not trivial. Furthermore, we give an example of topologically noneq...
Optimal estimates for the gradient of harmonic functions in the unit disk
Harmonic functions Bloch functions Hardy spaces.
2011/2/21
Concrete sharp constants in a pointwise estimate of the gradient of a harmonic function in the unit disk are obtained under the assumption that function belong to Hardy space hp, p > 1. This gen-erali...
Inequalities Involving Multipliers For Multivalent Harmonic Functions
Multivalent harmonic Multivalent harmonic starlike Multivalent harmonic convex Multiplier Integral convolution Neighborhood
2008/7/1
We introduce inequalities involving multipliers for complex-valued multivalent harmonic functions, using two sequences of positive real numbers. By specializing those sequences, we determine represent...
On Harmonic Functions by the Hadamard Product
Harmonic functions Hadamard product Extremal problems
2008/6/30
On Harmonic Functions by the Hadamard Product.
On Univalent Harmonic Functions
Convex harmonic functions Starlike harmonic functions Extremal problems
2008/6/27
On Univalent Harmonic Functions.
Univalent Harmonic Functions
Harmonic functions Dziok-Srivastava operator Convolution Integral operator Distortion bounds Neighborhood
2008/6/26
A necessary and sufficient coefficient is given for functions in a class of complex-valued harmonic univalent functions using the Dziok-Srivastava operator. Distortion bounds, extreme points, an integ...