Harnack Sets and Openness of Harmonie Morphisms.
Harnack's properties of biharmonic functions
Study of the equicontinuity of biharmonic functions, of the Harnack's principle and inequalities, and of their relations.
Harnacksche Kegel und Metrik in harmonischen Räumen.
Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map.
Hearing the shape of membranes: Further results.
Heat kernel of fractional Laplacian in cones
We give sharp estimates for the transition density of the isotropic stable Lévy process killed when leaving a right circular cone.
Heat kernel on manifolds with ends
We prove two-sided estimates of heat kernels on non-parabolic Riemannian manifolds with ends, assuming that the heat kernel on each end separately satisfies the Li-Yau estimate.
Heat sources and heat potentials
Henkin measures, Riesz products and singular sets
The mutual singularity problem for measures with restrictions on the spectrum is studied. The -pluriharmonic Riesz product construction on the complex sphere is introduced. Singular pluriharmonic measures supported by sets of maximal Hausdorff dimension are obtained.
Hermite and convexity.
Hessian measures. II.
High order representation formulas and embedding theorems on stratified groups and generalizations
We derive various integral representation formulas for a function minus a polynomial in terms of vector field gradients of the function of appropriately high order. Our results hold in the general setting of metric spaces, including those associated with Carnot-Carathéodory vector fields, under the assumption that a suitable to Poincaré inequality holds. Of particular interest are the representation formulas in Euclidean space and stratified groups, where polynomials exist and to Poincaré...
Hilbert transforms and the Cauchy integral in euclidean space
We generalize the notions of harmonic conjugate functions and Hilbert transforms to higher-dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These harmonic conjugates are in general far from being unique, but under suitable boundary conditions we prove existence and uniqueness of conjugates. The proof also yields invertibility results for a new class of generalized double layer potential operators on Lipschitz surfaces and boundedness of related Hilbert...
Hitting distributions domination and subordinate resolvents; an analytic approach
We give an analytic version of the well known Shih's theorem concerning the Markov processes whose hitting distributions are dominated by those of a given process. The treatment is purely analytic, completely different from Shih's arguments and improves essentially his result (in the case when the given processes are transient
Hölder continuity of normalized solutions of the Schrödínger equation.
Holomorphic extensions of formal objects
We are interested on families of formal power series in parameterized by (). If every is a polynomial whose degree is bounded by a linear function ( for some and ) then the family is either convergent or the series for all except a pluri-polar set. Generalizations of these results are provided for formal objects associated to germs of diffeomorphism (formal power series, formal meromorphic functions, etc.). We are interested on describing the nature of the set of parameters where...
Homogeneous extremal function for a ball in ℝ²
We point out relations between Siciak’s homogeneous extremal function and the Cauchy-Poisson transform in case is a ball in ℝ². In particular, we find effective formulas for for an important class of balls. These formulas imply that, in general, is not a norm in ℂ².
Homogeneous random measures and strongly supermedian kernels of a Markov process.
Hp (Rn) is equidistributed with Lp (Rn).
Hp-Spaces of Harmonic Functions and the Wiener Compactification.