Leon Happ

A fractional modular Poincar\'e--Wirtinger-type inequality in Sobolev spaces with variable exponents

Let $\Omega\subset\mathbb{R}^n$ be a bounded Lipschitz domain and let $p:\Omega\to[1,\infty)$ be a measurable, essentially bounded exponent; no regularity of $p$ -- in particular, no log-H\"older continuity -- is assumed. For a general non-negative measurable kernel $\mathcal{K}(x,y)$ admitting a radial bounding functi...