Series expansion of weighted Finsler–Kato–Hardy inequalities

In this work we consider weighted anisotropic Hardy inequalities and trace involving a general Finsler metric. We follow unifying approach, by establishing first sharp interpolation between them, extending the corresponding nonweighted version, being established recently different approach. Then, passing to bounded domains, obtain successive improvements adding remainder terms weights optimal constants, resulting in an infinite series-type improvement. The results extend, into context, earlier known ones within Euclidean setting. also discuss extension of our method case cones place half-space.