$L^p$ norm on the strip $\mathbb R\times[0,1)$ bounded by an $L^2$ slab amalgam norm plus $h^p$ times the gradient, $p\ge2$

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$L^p$ norm on the strip $\mathbb R\times[0,1)$ bounded by an $L^2$ slab amalgam norm plus $h^p$ times the gradient, $p\ge2$ · Prove2Me