Key points are not available for this paper at this time.
We show that the cone multiplier satisfies local Lᵖ-Lq bounds only in the trivial range 1 q 2 p. 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 B\'ekoll\'e and Bonami (Colloq. Math. 68, 1995, 81-100), regarding the continuity from Lᵖ Lq of the Cauchy-Szeg\"o projections associated with a class of bounded symmetric domains in Cⁿ with rank r2.
Yagüe et al. (Tue,) studied this question.