  We prove sharp power-weighted $L^p$, weak type and restricted weak type
inequalities for the heat semigroup maximal operator and Riesz transforms
associated with the Bessel operator $B_{\nu}$ in the exotic range of the
parameter $-\infty < \nu < 1$. Moreover, in the same framework, we characterize
basic mapping properties for other fundamental harmonic analysis operators,
including the heat semigroup based vertical $g$-function and fractional
integrals (Riesz potential operators).
