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We give in this short paper a sharp estimate for the norm of a multivariatedilation operator generated by multi-matrix (tensor) linear argumenttransformation (dilation operator) between two different weight Lebesgue-Rieszand Grand Lebesgue Spaces(GLS).  We consider also some examples and study the compactness of these operators.

Exact norm estimates for multivariate dilation operators between two Bilateral Weight Grand Lebesgue Spaces