Continuity properties of Riesz potentials and boundary limits of Beppo Levi functions.
Convergence in nonisotropic regions of harmonic functions in
We study the boundedness in of the projections onto spaces of functions with spectrum contained in horizontal strips. We obtain some results concerning convergence along nonisotropic regions of harmonic extensions of functions in with spectrum included in these horizontal strips.
Convergence of Balayage Measures.
Convex domains and unique continuation at the boundary.
We show that a harmonic function which vanishes continuously on an open set of the boundary of a convex domain cannot have a normal derivative which vanishes on a subset of positive surface measure. We also prove a similar result for caloric functions vanishing on the lateral boundary of a convex cylinder.
Correction to the paper “On weighted spaces” (Studia Math. 40 (1971), pp. 109-159)
Densité de l'intégrale d'aire dans Rn+ +1 et limites non tangentielles.
Dirchlet's problem on Green lines and some convergence theorems for Denjoy's domains.
Double layer potentials and the Dirichlet problem
Doubling conditions for harmonic measure in John domains
We introduce new classes of domains, i.e., semi-uniform domains and inner semi-uniform domains. Both of them are intermediate between the class of John domains and the class of uniform domains. Under the capacity density condition, we show that the harmonic measure of a John domain satisfies certain doubling conditions if and only if is a semi-uniform domain or an inner semi-uniform domain.
Estimates for derivatives of the Green functions on homogeneous manifolds of negative curvature.
Estimates for the Poisson kernels and their derivatives on rank one NA groups
For rank one solvable Lie groups of the type NA estimates for the Poisson kernels and their derivatives are obtained. The results give estimates on the Poisson kernel and its derivatives in a natural parametrization of the Poisson boundary (minus one point) of a general homogeneous, simply connected manifold of negative curvature.
Estimates of Green functions and harmonic measures for elliptic operators with singular drift terms.
Estimates of Green functions and their applications for parabolic operators with singular potentials
We prove global pointwise estimates for the Green function of a parabolic operator with potential in the parabolic Kato class on a cylindrical domain Ω. We apply these estimates to obtain a new and shorter proof of the Harnack inequality [16], and to study the boundary behavior of nonnegative solutions.
Fatou theorems and maximal functions for eigenfunctions of the Laplace-Beltrami operator in a bidisk.
Finding the conductors in circular networks from boundary measurements
Flatness of Domains and Doubling Properties of Measures Supported on their Boundary, with Applications to Harmonic Measure.
Free boundary regularity for harmonic measures and Poisson kernels.
Fundamental solutions of differential operators on homogeneous manifolds of negative curvature and related Riesz transforms
Generalized derivatives of an arbitrary order and the boundary properties of differentiated Poisson integrals for the half-space .
Growth and asymptotic sets of subharmonic functions (II)
We study the relation between the growth of a subharmonic function in the half space Rn+1+ and the size of its asymptotic set. In particular, we prove that for any n ≥ 1 and 0 < α ≤ n, there exists a subharmonic function u in the Rn+1+ satisfying the growth condition of order α : u(x) ≤ x-αn+1 for 0 < xn+1 < 1, such that the Hausdorff dimension of the asymptotic set ∪λ≠0A(λ) is exactly n-α. Here A(λ) is the set of boundary points at which f tends to λ along some curve. This...