For p∈(−∞, ∞) letQ p (∂Δ) be the space of all complex-valued functions f on the unit circle ∂Δ satisfying $$\mathop {\sup }\limits_{I \subset \partial \Delta } \left| I \right|^{ - p} \int_I {\int_I {\frac{{\left| {f(z) - f(w)} \right|^2 }}{{\left| {z - w} \right|^{2 - p} }}\left| {dz} \right|\left| {dw} \right|1, thenQ p (∂Δ)=BMO(∂Δ), the space of complex-valued functions with bounded mean oscillation on ∂Δ. Second, we prove that a function belongs toQ p (∂Δ) if and only if it is Mobius bounded in the Sobolev spaceL p 2 (∂Δ). Finally, a characterization ofQ p (∂Δ) is given via wavelets.