Calderón–Zygmund operators on amalgam spaces and in the discrete case

We prove the boundedness of Calderón–Zygmund operators on weighted amalgam spaces (Lp, q w)(Rn) for 1 < p,q <∞ with Muckenhoupt weights. To do this, we show the boundedness in the discrete case, i.e. the boundedness on q w(Zn). We also investigate on (Lp, ∞w )(Rn). As an application we consider an operator related to the Navier–Stokes equation. © 2007 Elsevier Inc. All rights reserved