${\cal H}^p$-spaces of harmonic functions

Harmonic functions in non-locally convex spaces

Harmonic Bergman Functions on Half-spaces

We study harmonic Bergman functions on the upper half-space of Rn. Among our main results are: The Bergman projection is bounded for the range 1 < p <∞; certain nonorthogonal projections are bounded for the range 1 ≤ p < ∞; the dual space of the Bergman L1-space is the harmonic Bloch space modulo constants; harmonic conjugation is bounded on the Bergman spaces for the range 1 ≤ p <∞; the Bergma...

A lower estimate of harmonic functions

We shall give a lower estimate of harmonic‎ ‎functions of order greater than one in a half space‎, ‎which‎ ‎generalize the result obtained by B‎. ‎Ya‎. ‎Levin in a half plane‎.

DIFFERENTIABILITY OF p-HARMONIC FUNCTIONS ON METRIC MEASURE SPACES

We study p-harmonic functions on metric measure spaces, which are formulated as minimizers to certain energy functionals. For spaces supporting a p-Poincaré inequality, we show that such functions satisfy an infinitesmal Lipschitz condition almost everywhere. This result is essentially sharp, since there are examples of metric spaces and p-harmonic functions that fail to be locally Lipschitz co...

Reproducing Kernels for Hilbert Spaces of Real Harmonic Functions

This paper studies a family of Hilbert spaces of real harmonic functions on bounded regions in Rn and will show that, for a range of values of s, they are reproducing kernel Hilbert spaces. The spaces are characterized by their boundary traces and the inner products are defined via their expansions in the harmonic Steklov eigenfunctions of the region. The reproducing kernels will then be descri...