We present elements of a theory of translation-invariant integration, measure, and harmonic analysis on a valuation field with local field as residue field, extending work of I. Fesenko. Applications to zeta integrals for two-dimensional local fields are then considered.
"Integration on Valuation Fields over Local Fields." Tokyo J. Math. 33 (1) 235 - 281, June 2010. https://doi.org/10.3836/tjm/1279719589