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The purpose of this paper is to present a general method that allows us to study exponential self-improving properties of generalized Poincaré inequalities associated with an approximation of the identity or a semigroup. In particular, we show the connection between our results and the JohnNirenberg theorem for the space BMO associated with approximations of the identity and semigroups.

Exponential self-improvement of generalized Poincaré inequalities associated with approximations of the identity and semigroups