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In this short article we introduce so-called anisotropic (weight) GrandLebesgue Spaces (more exactly, Grand Lebesgue-Riesz Spaces), which aregeneralization of the classical Lebesgue-Riesz Spaces and ordinary GrandLebesgue Spaces, and investigate the boundedness of weight Riesz potential andweight Fourier transforms in this spaces.

Multiple weight Riesz and Fourier transforms in bilateral anisotropic Grand Lebesgue spaces