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Restricted boundedness of translation operators on variable Lebesgue spaces
Published 29 Jul 2015 in math.FA | (1507.08089v5)
Abstract: In this paper, we investigate the inequality \begin{equation*} \left\Vert f(\cdot +h)\right\Vert_{p\left( \cdot \right) }\leq A\left\Vert f\right\Vert_{p\left( \cdot \right) },\quad h\in \mathbb{R}{n}, A>0 \end{equation*} under some suitable assumptions on the function $f$ and the variable exponent $p$.
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