Range characterization of the Ray Transform on Sobolev Spaces of Symmetric Tensor Fields in Two Dimensions

ABSTRACT

The ray transform integrates a symmetric rank tensor field on over lines. In the case of , the range characterization of the operator on weighted Sobolev spaces was obtained by Krishnan and Sharafutdinov. Here we obtain a range characterization result in higher‐order weighted Sobolev spaces in two dimensions. Range characterization in the case of is very different from that for , and this allows us to obtain such a result in higher order weighted Sobolev spaces for any real . Nevertheless, our main tool is again the Reshetnyak formula stating that for a solenoidal tensor field .