A GENERALIZATION OF A RESULT DUE TO HAVIN AND MAZÝA

Abstract

In this short note we give a direct proof of a generalization of a standard result due to Havin and Maz ya which relates the Bessel capacity of a set to its Hausdor dimension. Let L p (R d ) =ff : f = G g; g2 L p (R d )g, 2 R, p > 1, be the space of Bessel potentials, with normkfk;p =kgkp. Here G is the Bessel kernel, i.e., the inverse Fourier transform of the function ^