Wolff inequality in strongly nonlinear potential theory and applications (Q1769297)

The results are established in the framework of ``strong'' nonlinear potential theory: the underlying space is a Orlicz space. A Wolff-type inequality [see \textit{L. I. Hedberg} and \textit{Th. H. Wolff}, Ann. Inst. Fourier 33, No. 4, 161--187 (1983; Zbl 0508.31008)] for potentials associated with the Riesz and Bessel kernels is proved. As an application, the relation with the Hausdorff measure is established. Also, in the case of reflexive Orlicz spaces, it is proved that the Riesz and Bessel capacities decrease under orthogonal projections.