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We study a family of fractional Hardy-type inequalities \\begin{equation} \\frac{c_{N,s}}{2}\\displaystyle\\iint_{\\Omega\\times\\Omega}\\frac{(u(x)-u(y))^2}{|x-y|^{N+2s}}\\ dxdy-\\displaystyle\\lambda\\int_{\\Omega}u^2\\ dx\\geq C\\displaystyle\\int_{\\Omega}\\frac{u^2}{\\delta^{2s}}\\ dx,~~~\\quad\\forall\\lambda\\in\\mathbb{R},~~~~~~~(0.1) \\end{equation} with $u\\in C_c^\\infty(\\Omega)$ and $C=C(\\Omega,s,N,\\lambda)>0$. 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