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Abstract. We prove sharp power-weighted L p , weak type and restricted weak type inequalities for the heat and Poisson integral maximal operators, Riesz transform and a Littlewood-Paley type square function, emerging naturally in the harmonic analysis related to Bessel operators.

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As Fefferman and Stein showed, there is a tight connection between Carleson measures and BMO functions. In this work we extend this type of results to the more general scope of the BMO ϕ (ω) spaces. As a byproduct a weighted version of the Triebel-Lizorkin spaceḞ 0∞,2 is introduced, which turns out to be isomorphic to BMO(ω) as in the unweighted case.