Generalized Hardy inequalities

We show that the generalized Hardy inequality k |bkfˆ(nk)| C f H1 holds for f ∈ H1 and certain (bk) ∈ lr (2 q ∞) whenever (nk)∞k =1 ⊂ N satisfies appropriate growth conditions dependent on r.  2003 Elsevier Inc. All rights reserved.