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