Weighted log-rank tests are arguably the most widely used tests by\npractitioners for the two-sample problem in the context of right-censored data.\nMany approaches have been considered to make weighted log-rank tests more\nrobust against a broader family of alternatives, among them, considering linear\ncombinations of weighted log-rank tests, and taking the maximum among a finite\ncollection of them. In this paper, we propose as test statistic the supremum of\na collection of (potentially infinite) weight-indexed log-rank tests where the\nindex space is the unit ball in a reproducing kernel Hilbert space (RKHS). By\nusing some desirable properties of RKHSs we provide an exact and simple\nevaluation of the test statistic and establish connections with previous tests\nin the literature. Additionally, we show that for a special family of RKHSs,\nthe proposed test is omnibus. We finalise by performing an empirical evaluation\nof the proposed methodology and show an application to a real data scenario.\nOur theoretical results are proved using techniques for double integrals with\nrespect to martingales that may be of independent interest.\n