Abstract In this paper we prove Fefferman's inequalities associated to potentials belonging
to a generalized Morrey space or a Stummel class.
We also show that the logarithm of a non-negative weak solution to a second order elliptic partial differential equation
with potential in a generalized Morrey space or a Stummel class, under some assumptions, belongs to the bounded mean oscillation class.
As a consequence, this elliptic partial differential equation has the strong unique continuation property.
An example of an elliptic partial differential equation with potential in a Morrey space
or a Stummel class which does not satisfy the strong unique continuation is presented. 
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