On a condition of thinness at infinity
On a conjecture of Král concerning the subharmonic extension of continuously differentiable functions
This note verifies a conjecture of Král, that a continuously differentiable function, which is subharmonic outside its critical set, is subharmonic everywhere.
On a direct decomposition of the space .
On a generalized heat potential
On a generalized reflection law for functions satisfying the Helmholtz equation.
On a maximum principle in potential theory
On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball
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.
On a theorem of Cartan
On a theorem of M. G. Arsove
On a version of Littlewood-Paley function
On approach regions for the conjugate Poisson integral and singular integrals
Let ũ denote the conjugate Poisson integral of a function . We give conditions on a region Ω so that , the Hilbert transform of f at x, for a.e. x. We also consider more general Calderón-Zygmund singular integrals and give conditions on a set Ω so that is a bounded operator on , 1 < p < ∞, and is weak (1,1).
On Boundary Behaviour of Harmonic Functions in Hölder Domains.
On boundary Harnack principles and poles of extremal harmonic functions.
On certain oscillatory properties for solutions of an equation with a biharmonic leading part
On certain reflexion principes
On coincidence of p-module of a family of curves and p-capacity on the Carnot group.
The notion of the extremal length and the module of families of curves has been studied extensively and has given rise to a lot of applications to complex analysis and the potential theory. In particular, the coincidence of the p-module and the p-capacity plays an mportant role. We consider this problem on the Carnot group. The Carnot group G is a simply connected nilpotent Lie group equipped vith an appropriate family of dilations. Let omega be a bounded domain on G and Ko, K1 be disjoint non-empty...
On definitions of superharmonic functions
Let be an elliptic differential operator of second order with variable coefficients. In this paper it is proved that any -superharmonic function in the Riesz-Brelot sense is locally summable and satisfies the -superharmonicity in the sense of Schwartz distribution.
On duality and interpolation for spaces of polyharmonic functions
On essential norm of the Neumann operator
One of the classical methods of solving the Dirichlet problem and the Neumann problem in is the method of integral equations. If we wish to use the Fredholm-Radon theory to solve the problem, it is useful to estimate the essential norm of the Neumann operator with respect to a norm on the space of continuous functions on the boundary of the domain investigated, where this norm is equivalent to the maximum norm. It is shown in the paper that under a deformation of the domain investigated by a diffeomorphism,...
On Exceptional Sets for Superharmonic Functions in a Halfspace: An Inverse Problem.