The "refinement" terminology in connection with Christ's <A HREF="https://math.berkeley.edu/~mchrist/Papers/kielslides.pdf" title="Convolution, curvature and a bit of combinatorics">1998 paper</A> seems to originate from Tao and Wright's <a href="https://arxiv.org/abs/math/0108137" title="L^p improving bounds for averages along curves">2001 article</a>, although the earliest explicit reference to "Christ's method of refinements" I could locate is a <A HREF="https://www.semanticscholar.org/paper/A-non-linear-generalisation-of-the-Loomis-Whitney-Bennett-Carbery/fc2039a582e16fb3d5364057af8e58827655e55d" title="Bennett, Carbey, and Wright - A non-linear generalisation of the Loomis–Whitney inequality and applications">2005 article</A>.

Christ himself speaks of a "refined band structure".