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Magdalena Sobczak-Kneć, Viktor Starkov, Jan Szynal (2011)
Annales UMCS, Mathematica
The relation between the Jacobian and the orders of a linear invariant family of locally univalent harmonic mapping in the plane is studied. The new order (called the strong order) of a linear invariant family is defined and the relations between order and strong order are established.
Miroslav Dont (1975)
Czechoslovak Mathematical Journal
G. A. Camera (1989)
Compositio Mathematica
Stephen J. Gardiner, Tomas Sjödin (2020)
Mathematica Bohemica
This note verifies a conjecture of Král, that a continuously differentiable function, which is subharmonic outside its critical set, is subharmonic everywhere.
Yoichi Oshima (1992)
Forum mathematicum
Kähler, U. (1999)
Zeitschrift für Analysis und ihre Anwendungen
Yitzhak Weit (1991)
Aequationes mathematicae
Jiří Veselý (1975)
Czechoslovak Mathematical Journal
Victor Anandam, Marcel Brelot (1981)
Annales Polonici Mathematici
Aberra, Dawit (1999)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Miroslav Dont (1975)
Czechoslovak Mathematical Journal
Miroslav Dont (1973)
Commentationes Mathematicae Universitatis Carolinae
David Eric Edmunds, Jiří Rákosník (1999)
Mathematica Bohemica
The Hardy inequality with holds for if is an open set with a sufficiently smooth boundary and if . P. Hajlasz proved the pointwise counterpart to this inequality involving a maximal function of Hardy-Littlewood type on the right hand side and, as a consequence, obtained the integral Hardy inequality. We extend these results for gradients of higher order and also for .
Dagmar Medková (1982)
Časopis pro pěstování matematiky
Vladimír Drápalík, Vladimír Janovský (1988)
Aplikace matematiky
Daoud Bshouty, Abdallah Lyzzaik (2012)
Annales UMCS, Mathematica
The aim of this work is to answer positively a more general question than the following which is due to T. Sheil-Small: Does the harmonic extension in the open unit disc of a mapping f from the unit circle into itself of the form f(eit) = eiϕ(t), 0 ≤ t ≤ 2π, where ϕ is a continuously non-decreasing function that satisfies ϕ(2π)−ϕ(0) = 2Nπ, assume every value finitely many times in the disc?
Dariusz Partyka, Ken-ichi Sakan (2012)
Annales UMCS, Mathematica
In 1984 J. Clunie and T. Sheil-Small proved ([2, Corollary 5.8]) that for any complex-valued and sense-preserving injective harmonic mapping F in the unit disk D, if F(D) is a convex domain, then the inequality |G(z2)− G(z1)| < |H(z2) − H(z1)| holds for all distinct points z1, z2∈ D. Here H and G are holomorphic mappings in D determined by F = H + Ḡ, up to a constant function. We extend this inequality by replacing the unit disk by an arbitrary nonempty domain Ω in ℂ and improve it provided F...
Bezzarga, Mounir, Kefi, Khaled (2005)
Fractional Calculus and Applied Analysis
2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05We study a singular value problem and the boundary Harnack principle for the fractional Laplacian on the exterior of the unit ball.
Dixit, K.K., Porwal, Saurabh (2009)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Bishop, Christopher J. (1996)
Annales Academiae Scientiarum Fennicae. Mathematica