Brezis–Marcus type inequalities with Lamb constant

Hardy-type inequalities with an additional term are proved for compactly supported smooth functions on open convex sets in the Euclidean space. We obtain one-dimensional $L_p$-inequalities and their multidimensional analogs on arbitrary domains, on regular sets, on domains with $\theta$-cone condition and on convex domains. We use Bessel's function and the Lamb constant.