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$%E. Romera, Extremal vector vInequalities for Hankel transforms, Rev. Mat. Complut. 22 (2009), no. 1, 153–163.%$
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 when . Here we prove that there exist weak-type estimates for this operator for the extremal exponents, that is, it is bounded from to for when , , , and we consider radial functions.
Key words: disc multiplier, Fourier-Hankel transforms.
2000 Mathematics Subject Classification: 42B10.