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H -cones and potential theory

Nicu Boboc, Gheorghe Bucur, A. Cornea (1975)

Annales de l'institut Fourier

The H -cone is an abstract model for the cone of positive superharmonic functions on a harmonic space or for the cone of excessive functions with respect to a resolvent family, having sufficiently many properties in order to develop a good deal of balayage theory and also to construct a dual concept which is also an H -cone. There are given an integral representation theorem and a representation theorem as an H -cone of functions for which fine topology, thinnes, negligible sets and the sheaf property...

Hardy spaces and the Dirichlet problem on Lipschitz domains.

Carlos E. Kenig, Jill Pipher (1987)

Revista Matemática Iberoamericana

Our concern in this paper is to describe a class of Hardy spaces Hp(D) for 1 ≤ p < 2 on a Lipschitz domain D ⊂ Rn when n ≥ 3, and a certain smooth counterpart of Hp(D) on Rn-1, by providing an atomic decomposition and a description of their duals.

Hardy spaces for the Laplacian with lower order perturbations

Tomasz Luks (2011)

Studia Mathematica

We consider Hardy spaces of functions harmonic on smooth domains in Euclidean spaces of dimension greater than two with respect to the Laplacian perturbed by lower order terms. We deal with the gradient and Schrödinger perturbations under appropriate Kato conditions. In this context we show the usual correspondence between the harmonic Hardy spaces and the L p spaces (or the space of finite measures if p = 1) on the boundary. To this end we prove the uniform comparability of the respective harmonic...

Harmonic deformability of planar curves

Eleutherius Symeonidis (2021)

Commentationes Mathematicae Universitatis Carolinae

We study the formerly established concept of deformation of a planar curve and clarify its applicability and range. We present several applications on classical curves.

Harmonic functions on classical rank one balls

Philippe Jaming (2001)

Bollettino dell'Unione Matematica Italiana

In questo articolo studieremo le relazioni fra le funzioni armoniche nella palla iperbolica (sia essa reale, complessa o quaternionica), le funzione armoniche euclidee in questa palla, e le funzione pluriarmoniche sotto certe condizioni di crescita. In particolare, estenderemo al caso quaternionico risultati anteriori dell'autore (nel caso reale), e di A. Bonami, J. Bruna e S. Grellier (nel caso complesso).

Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces

Philippe Jaming (1999)

Colloquium Mathematicae

We study harmonic functions for the Laplace-eltrami operator on the real hyperbolic space n . We obtain necessary and sufficient conditions for these functions and their normal derivatives to have a boundary distribution. In doing so, we consider different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball n . We then study the Hardy spaces H p ( n ) , 0

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