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

Abstract

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.

References in corpus (3)

• Riesz's and Bessel's Operators in Bilateral Grand Lebesgue Spaces
• Nikol'skii-type inequalities for rearrangement invariant spaces
• One and two weight norm inequalities for Riesz potentials

Cited by in corpus (5)

• Hardy's operator and normability of generalized Lorentz-Marcinkiewicz spaces, with sharp or weakly sharp constant estimation
• Exact norm estimates for multivariate dilation operators between two Bilateral Weight Grand Lebesgue Spaces
• Sharp estimates for module of continuity of fractional integrals and derivatives
• Lebesgue spaces norm estimates for fractional integrals and derivatives
• Lebesgue-Riesz norm estimates for fractional Laplace transform