A Wiener criterion and the Lebesgue property for a broad class of generalized potentials

In this talk, we study a wide class of generalized potentials in the complex plane generated by singular kernels that are non-increasing, convex, and satisfy a doubling condition. We establish an analogue of the Wiener criterion and characterize thin sets via a discrete Wiener-type series in terms of generalized capacity. This framework unifies classical subharmonic and Riesz potentials, as well as certain oscillating potentials. As an application, we prove that the restriction of any bounded generalized potential to a real line has the Lebesgue property at every point.