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We study ray transforms on spherically symmetric manifolds with a piecewise$C^{1,1}$ metric. Assuming the Herglotz condition, the X-ray transform isinjective on the space of $L^2$ functions on such manifolds. We also proveinjectivity results for broken ray transforms (with and without periodicity) onsuch manifolds with a $C^{1,1}$ metric. To make these problems tractable in lowregularity, we introduce and study a class of generalized Abel transforms andstudy their properties. This low regularity setting is relevant for geophysicalapplications.

Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds