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 $i\tfrac{\partial u}{\partial t}=D^βu$ 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 $\mathbb{R}^+$. The main tools are a sumability 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.

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