Research proof index

John-Nirenberg iteration from a base level. This is a variant of john_nirenberg (and john_nirenberg_iteration) where the one-step decay hypothesis h_decay is only assumed for lam ≥ A (instead of for all lam > 0). The exponential decay conclusion holds for all t > 0, with a slightly larger constant prefactor 1/θ² to absorb the base case `...

Iteration of level-set decay to exponential decay.

Iterating one-step level-set decay gives a geometric bound.

Exponential domination for the discrete John-Nirenberg iteration.

Geometric decay of selected John-Nirenberg bad-ball unions from the local half-measure step.

An a.e. lower bound on the half ball upgrades to an essential-infimum bound on the half ball.