We describe a parallel implementation of a compressible Lattice Boltzmann code on a multi-GPU cluster based on Nvidia Fermi processors. We analyze how to optimize the algorithm for GP-GPU architectures, describe the implementation choices that we have adopted and compare our performance results with an implementation optimized for latest generation multi-core CPUs. Our program runs at approximate to 30% of the double-precision peak performance of one GPU and shows almost linear scaling when run on the multi-GPU cluster.

We prove continuity of the Riesz potential operator in optimal couples orf rearrangement invariant function spaces defined in R^n with the Lebesgue measure. An applicationis given to the Hardy-Littlewood maximal operator

We give a decomposition for the dual space of some Banach Function Spaces as the Zygmund space EXP_alpha of the exponential integrable functions, the Marcinkiewicz spaceL^p,infty, and the Grand Lebesgue Space L^p),Theta