Failure of strong unique continuation for harmonic functions on RCD 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 Fatou-type Theorem for Harmonic Functions on Symmetric Spaces

Corrigenda to “unique Continuation for Schrödinger Operators” and a Remark on Interpolation of Morrey Spaces

The purpose of this note is twofold. First it is a corrigenda of our paper [RV1]. And secondly we make some remarks concerning the interpolation properties of Morrey spaces. 1. Corrigenda. In our paper “Unique continuation for Schrödinger operators with potential in Morrey spaces” [RV1], we claimed the following statement with the name of Theorem 1 —see (5), (6) below for the necessary definiti...

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...

Stability for certain subclasses of harmonic univalent functions

In this paper, the problem of stability for certain subclasses of harmonic univalent functions is investigated. Some lower bounds for the radius of stability of these subclasses are found.