... p, then |u(·)|p/|·|q∈L1(Rn) for every u ∈ W1,p(Rn).Furthermore,Rnu(·)p|·|qdx pn − qqup−qLp∇uqLp, (1.1) for every u∈ W1,p(Rn).It is easy ... equivalent definitions and norms for Besov spaceneeded in this paper. The reader is referred to the well-known books of Runst and Sickel[5], Triebel [6], and Miao [4] for details.Hindawi Publishing ... precise proposition substituting˙Fs2,2=˙Bs2,2 for ˙Bs2,1.(v) The Hardy-type inequality w ill be excellent substituting˙Fsp,2 for ˙Bsp,1, but it failsusing this method, in fact...