Local cone multipliers and Cauchy–Szegö projections in bounded symmetric domains

We show that the cone multiplier satisfies local ‐ bounds only in the trivial range . To do so, we suitably adapt to this setting the proof of Fefferman for the ball multiplier. As a consequence we answer negatively a question by Békollé and Bonami, regarding the continuity from of the Cauchy–Szegö projections associated with a class of bounded symmetric domains in with rank .