Lower-dimensional Fefferman measures via the Bergman kernel

Motivated by the theory of Hausdorff measures, we propose a new construction of the Fefferman hypersurface measure. This construction reveals the existence of non-trivial Fefferman-type measures on the boundary of some domains such as products of balls - which are outside the purview of Fefferman's original definition. We also show that these measures enjoy certain transformation properties under biholomorphic mappings.