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Bessel Potential Space inequality

The Bessel Potential Space is defined for $s\in\mathbb{R}$ as, $H^s(\mathbb{R}^d) = \{f\in L_2(\mathbb{R}^n) : (1+|\cdot|)^{s/2}\hat{f}(\cdot)\in L_2(\mathbb{R}^n)\}. $ This defines a Hilbert space ...