Borinium, borenium, and boronium ions: synthesis, reactivity, and applications

Boron cations are elusive and highly electrophilic species that play a key role in the chemistry of boron. Despite early interest in the chemistry of boron cations, until recently they have largely remained chemical curiosities. However, hints at harnessing their potential as potent electrophiles have begun to appear and developments in weakly coordinating anion technology suggest that this is an area of research that is ripe for exploration. It has been nearly 20 years since the last major review on boron cations; herein we summarize the progress in the area since that time.     

Ideal weights: Asymptotically optimal versions of doubling, absolute continuity, and bounded mean oscillation

Sharp inequalities between weight bounds (from the doubling, A_p, and reverse Hölder conditions) and the BMO norm are obtained when the former are near their optimal values. In particular, the BMO norm of the logarithm of a weight is controlled by the square root of the logarithm of its A_∞ bound. These estimates lead to a systematic development of asymptotically sharp higher integrability results for reverse Hölder weights and extend Coifman and Fefferman's formulation of the A_∞ condition as an equivalence relation on doubling measures to the setting in which all bounds become optimal over small scales.