Hardy spaces associated with semigroups generated by bessel operators with potentials Academic Article

Let {Tt}t>0 be the semigroup of linear operators generated by the operator - u(x) = (1/2)u(x) + (/2x)u(x) - V(x)u(x), x > 0, where V is a nonnegative potential satisfying a certain regularity condition, > 1. We say that a function f belongs to the Hardy space H1associated with the semigroup Ttif the maximal function supt>0|Ttf(x)| belongs to L1((0,), xdx). We prove atomic decompositions for the elements of the Hardy space H1. 2008 University of Houston.

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