Extremal Vector Valued Inequalities for Hankel Transforms

Abstract

The disc multiplier may be seen as a vector valued operator when we consider its projections in terms of the spherical harmonics. In this form, it represents a vector valued Hankel transform. We know that, for radial functions, it is bounded on the spaces. Here we prove that there exist weak-type estimates for this operator for the extremal exponents, that is, it is bounded from L, p0 < q < p1, and we consider radial functions.