We characterise some classes of bounded linear and compact operators from the spaces of sequences that are strongly summable or strongly summable to zero with index p ≥ 1 by the Cesaro method of order 1 into the generalised Hahn space. Furthermore, we establish estimates for the norm and the Hausdorff measure of noncompactness of those operators. Our results are complementary to recently published dual corresponding results with the order of the sequence spaces reversed. We also apply our results to the graphical representations of related potential surfaces and the corresponding Wulff’s crystals.