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In this paper we show that if $\\ell\\in \\mathbb{R}$ satisfies $0< \\ell <N$ and $\\ell \\leq \\nu$, then the estimate \\begin{equation}\\nonumber \\left(\\int_{\\mathbb{R}^{N}}| (-\\Delta)^{(\\nu-\\ell)/2}u(x)|^{q}|x|^{-N+(N-\\ell)q}\\,dx\\right)^{1/q}\\leq C \\|A(D)u\\|_{L^{1}} \\end{equation} holds for every $u \\in C_{c}^{\\infty}(\\mathbb{R}^{N};E)$ and $1\\le q<\\frac{N}{N-\\ell}$ if and only if $A(D)$ is canceling in the sense of V. 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