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The purpose of this paper is to continue the study of the so-called holomorphic  Q  classes via two conformal deformations of the fractional image area of a holomorphic function on the open unit disk. Results include fractional order Carleson measures, embeddings of Choquet spaces with respect to Hausdorff capacities, preduals, strong isoperimetric inequalities, boundary values, harmonic extensions, Brownian motions, function modules, value distributions, and harmonic majorants of solutions to Euler-Lagrange differential equation subject to finite conformally invariant energy with fractional order.

Some results on Q p spaces, 0 < p < 1, continued