Helena F. Goncalves, Henning Kempka: Non-smooth atomic decomposition of 2-microlocal spaces and application to pointwise multipliers

Author(s):

Helena F. Goncalves
Henning Kempka

Title:

Helena F. Goncalves, Henning Kempka: Non-smooth atomic decomposition of 2-microlocal spaces and application to pointwise multipliers

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 15, 2015

Mathematics Subject Classification:

    none []

Abstract:

We provide non-smooth atomic characterizations for 2-microlocal Besov and Triebel–Lizorkin spaces with variable integrability$B^{w}_{p(\cdot),q(\cdot)}(\mathbb{R}^n)$ and $B^{w}_{p(\cdot),q(\cdot)}(\mathbb{R}^n)$. These spaces cover the classical Besov and Triebel–Lizorkin spaces as well as spaces of variable smoothness and integrability. As an application, we state a pointwise multipliers result for these spaces.

Keywords:

2-microlocal spaces, Besov and Triebel–Lizorkin spaces, Variable integrability, Atomic decomposition, Pointwise multipliers

Language:

English

Publication time:

09/2015