Optimal Embeddings of Bessel-Potential-Type Spaces into Generalized Holder Spaces Involving k-Modulus of Smoothness

摘要

We establish necessary and sufficient conditions for embeddings of Bessel potential spaces H-sigma X (IRn) with order of smoothness sigma is an element of (0, n), modelled upon rearrangement invariant Banach function spaces X (IRn), into generalized Holder spaces (involving k-modulus of smoothness). We apply our results to the case when X (IRn) is the Lorentz-Karamata space L-p,L-q;b (IRn). In particular, we are able to characterize optimal embeddings of Bessel potential spaces H-sigma L-p,L-q;b (IRn) into generalized Holder spaces. Applications cover both superlimiting and limiting cases. We also show that our results yield new and sharp embeddings of Sobolev-Orlicz spaces (Wk+1Ln/k)(log L)(alpha)(IRn) and (WLn/k)-L-k(log L)(alpha)(IRn) into generalized Holder spaces.