A note on the relative growth of products of multiple partial quotients in the plane

Let {equation presented} be the continued fraction expansion of a real number r ∈ R. The growth properties of the products of consecutive partial quotients are tied up with the set admitting improvements to Dirichlet's theorem. Let {equation presented}, and let {equation presented} be a function such that {equation presented} as n → ∞. We calculate the Hausdorff dimension of the set of all (x,y) ∈ [0,1)2 such that {equation presented} is satisfied for all n ≥ 1.