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

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