  An important inequality due to Wolff on plate decompositions of cone
multipliers is known to have consequences for a variety of problems in harmonic
analysis. We observe that the range in Wolff's inequality, for the conic and
the spherical versions, can be improved by using bilinear restriction results.
We also use this inequality to give some improved estimates on square functions
associated to decompositions of cone multipliers in low dimensions. This gives
a new L^4 bound for the cone multiplier operator in three dimensions.
