Conjugacy for Fourier-Bessel expansions

We define and investigate the conjugate operator for Fourier-Bessel expansions. Weighted norm and weak type (1, 1) inequalities are proved for this operator by using a local version of the Calderón-Zygmund theory, with weights in most cases more general than Ap weights. Also results on Poisson and conjugate Poisson integrals are furnished for the expansions considered. Finally, an alternative conjugate operator is discussed