B. Bongioanni

On dyadic nonlocal Schrödinger equations with Besov initial data

Abstract In this paper we consider the pointwise convergence to the initial data for the Schrodinger–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 Calderon sharp maximal operator.

Nonlocal Schrödinger equations in metric measure spaces

Abstract In this note we consider the pointwise convergence to the initial data for the solutions of some nonlocal dyadic Schrodinger equations on spaces of homogeneous type. We prove the a.e. convergence when the initial data belongs to a dyadic version of an L 2 based Besov space.