Improved Versions of Some Furstenberg Type Slicing Theorems for Self-Affine Carpets

Let F be a Bedford-McMullen carpet defined by independent integer exponents. We prove that for every line l subset of R-2 not parallel to the major axes, dim(H)(l boolean AND F) <= max {0, dim(H) f/dim*F center dot (dim*F-1)} and dim(P)(l boolean AND F) <= max{0, dim(P)F/dim*F center dot (dim*F-1)}, where dim* is Furstenberg's star dimension (maximal dimension of microsets). This improves the state-of-the-art results on Furstenberg type slicing Theorems for affine invariant carpets.