Rotational smoothing

Rotational smoothing is a phenomenon consisting in gain of regularity by means averaging over rotations. This present operators that regularize only certain directions, contrast to regularizing all directions. The the result rotating directions where corresponding operator performs effect. In this paper we carry out systematic study rotational for class includes k-vector-space Riesz potentials Rn with k<n, and convolution fundamental solutions elliptic constant-coefficient differential acting on k-dimensional linear subspaces. Examples latter type are planar Cauchy transform Rn, or solution transport equation Rn. analysis motivated resolution some inverse problems under low-regularity assumptions.