Adam Sikora

activity

20062025

collaborators

5 papers

math.AP2025

On the Interplay Between Hodge Projections and Bounded Harmonic Functions on Manifolds with Ends

Dangyang He, Adam Sikora

We investigate the $L^{p}$ -boundedness of the Hodge projection in the setting of manifolds with ends. We examine its relationship to the Riesz transform and the space of bounded harm…

math.FA2024

Harmonic functions for Bessel operators

Michał Dymowski, Marcin Preisner, Adam Sikora

We verify the continuity of the Riesz transform from the operator related Hardy space to $L^{1}$ - Lebesgue space of integrable functions. For the standard Euclidean Laplace operator…

math.AP2024

Regularity and Separation for $p$ -Laplace operators

Daniel Hauer, Adam Sikora

We analyze $p$ -Laplace operators with degenerate elliptic coefficients. This investigation includes Grušin type $p$ -Laplace operators. We describe a \emph{separation phenomenon} in…

math.AP2019

Riesz transforms on a class of non-doubling manifolds II

Andrew Hassell, Daniel Nix, Adam Sikora

We consider a class of manifolds $M$ obtained by taking the connected sum of a finite number of $N$ -dimensional Riemannian manifolds of the form $(\mathbb{R}^{n_i}, δ) \t…

math.AP2006

Second-order operators with degenerate coefficients

A. F. M. ter Elst, Derek W. Robinson, Adam Sikora +1

We consider properties of second-order operators $H = - \sum_{i, j = 1}^{d} \partial_{i} c_{ij} \partial_{j}$ on $\Ri^d$ with bounded real symmetric measurable coefficients. We assume…