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In this paper we investigate the extension of high energy resummation at LLxaccuracy to jet observables. In particular, we present the high energy resummedexpression of the transverse momentum distribution of the outgoing parton inthe general partonic process $g(q) + g(q) \to g(q) + X$. In order to reach thisresult, several new ideas are introduced and exploited. First we prove that LLxresummation is achieved by dressing with hard radiation an off-shell gluoninitiated LO process even if its on-shell limit is vanishing or trivial. Thenwe present a gauge-invariant framework where these calculations can beperformed by using the modern helicity techniques. Finally, we show a possibleway to restore gluon indistinguishability in the final state, which isotherwise lost in the resummation procedure, at all orders in $\alpha_s$ atLLx. All partonic channels are then resummed and cross-checked againstfixed-order calculations up to $\mathcal{O}(\alpha_s^3)$

High Energy Resummation of Jet Observables