On dyadic nonlocal Schrِdinger 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 = D β u with u ( x , 0 ) = u 0 in a dyadic Besov space. Here D β denotes the fractional derivative of order β associated to the dyadic distance δ on R + . The main tools are a summability formula for the kernel of D β and pointwise estimates of the corresponding maximal operator in terms of the dyadic Hardy–Littlewood function and the Calderón sharp maximal operator.