Calderon-Zygmund operators on amalgam spaces and in the discrete case

We prove the boundedness of Calderon-Zygmund operators on weighted amalgam spaces (L-p, l(w)(q))(R-n) for 1 < p, q < infinity with Muckenhoupt weights. To do this, we show the boundedness in the discrete case, i.e. the boundedness on l(w)(q) (Z(n)). We also investigate on (L-p, l(w)(infinity)) (R-n). As an application we consider an operator related to the Navier-Stokes equation. (C) 2007 Elsevier Inc. All rights reserved.