Sobolev-BMO and Fractional Integrals and Global Weighted Lorentz Estimates with Embeddings of Weighted Integral Means

Abstract

The embeddings and duality theorems between classical Lorentz spaces and the characterization of associate spaces of generalized weighted weak-Lorentz spaces with Lorentz-type spaces involvingweighted integral means are shown. The higher integrability for parabolic systems of P-Laplacian type, Lorentz estimates for degenerateand singular evolutionary systems are determined. The nonlinear gradient and global weighted Lorentz estimates for parabolic obstacle problems and to nonlinear parabolic equations in nonsmooth domains are obtained. We deal with the traces of Tjmo-Sobolev spaces and investigate the boundedness, the multilinear estimates, Sobolev - BMO and the fractional integrals on Lipschitz spaces and on super-critical ranges of Lebesgue spaces.