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G_\\mu=\\overset{d}{\\underset{i=1}{\\sum}}\\partial_{x_i}^2+\\left(\\overset{d}{\\underset{i=1}{\\sum}}x_i^2\\right)^{2\\mu}\\overset{k}{\\underset{j=1}{\\sum}}\\partial_{y_j}^2. \\end{equation*} and derive weighted Hardy-Sobolev type inequalities and weighted Caffarelli-Kohn-Nirenberg type inequalities related to 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