  The Cauchy problem for the Maxwell-Klein-Gordon equations in Lorenz gauge in
two and three space dimensions is locally well-posed for low regularity data
without finite energy. The result relies on the null structure for the main
bilinear terms which was shown to be not only present in Coulomb gauge but also
in Lorenz gauge by Selberg and Tesfahun, who proved global well-posedness for
finite energy data in three space dimensions. This null structure is combined
with product estimates for wave-Sobolev spaces given systematically by
d'Ancona, Foschi and Selberg.
