Full paper in PDF format:
$%E. Romera, Extremal vector vInequalities for Hankel transforms, Rev. Mat. Complut. 22 (2009), no. 1, 153–163.%$

Extremal Vector Valued Inequalities for Hankel Transforms
Departamento de Matemáticas
Universidad Carlos III de Madrid
Avenida de la Universidad, 30
28911 Leganés (Madrid) — Spain


Received: February 15, 2008
Accepted: June 5, 2008


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 Lpq(rn-1dr)
 l  when -2n-< p,q <-2n
n+1       n-1  . Here we prove that there exist weak-type estimates for this operator for the extremal exponents, that is, it is bounded from Lpilq,1(rn-1dr)  to Lpliq,∞(rn-1dr)  for i= 0,1  when p0 = 2nn+1  , p1 = 2nn-1  , p0 < q < p1  , and we consider radial functions.

Key words: disc multiplier, Fourier-Hankel transforms.
2000 Mathematics Subject Classification: