  We study weak-type estimates and exponential integrability for the variable
order Riesz potential. As an application we prove an exponential integrability
result with respect to the Hausdorff content for functions from variable
exponent Sobolev spaces. In particular, the earlier exponential integrability
results are improved to a corresponding one with respect to the Choque integral
whenever John domains are considered. Moreover, new exponential integrability
results also for domains with outward cusps are obtained.
