On dyadic nonlocal Schrödinger equations with Besov initial data

In this paper we consider the pointwise convergence to the initial data for the Schrödinger–Dirac equation i∂u∂t=Dβu with u(x,0)=u0u(x,0)=u0 in a dyadic Besov space. Here DβDβ denotes the fractional derivative of order ββ associated to the dyadic distance δδ on R+R+. The main tools are a summability formula for the kernel of DβDβ and pointwise estimates of the corresponding maximal operator in terms of the dyadic Hardy–Littlewood function and the Calderón sharp maximal operator.