Upper bounds are obtained for the p-capacity of compact sets in \({\mathbb {R}}^d\) , with \(d \ge 2\) and \(1<p<d\) . Upper and lower bounds are obtained for the product of p-capacity and powers of the q-torsional rigidity over the collection of all non-empty, open, bounded and convex sets in \({\mathbb {R}}^d\) with either a perimeter constraint, or a measure constraint, or a combination of perimeter and measure constraints. For some range of parameters we identify the ball as the unique (up to homotheties) maximiser or minimiser respectively.
