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The paper gives sharp pointwise estimates for functions belonging to \(\dot{H}^{s,p}(\mathbb {R}^N)\) with radial symmetry in m blocks of variables, for \(m<sp<N\). The estimates are formulated in terms of multiradial monomials. The form of the monomials depends on the structure of the group of block-radial symmetries and the distances of the given point to the hyperplanes in \(\mathbb {R}^N\) that contain the singular orbits of the group. For some exceptional set of parameters the logarithmic factor is needed. Weak continuity related to the estimates is also considered.

Pointwise Estimates for Block-Radial Functions of Sobolev Classes