Abstract:

For a class of linear operators including Riesz potentials on R^d
with a non-negative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces
is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates.

Key words: Riesz potential, Lebesgue space, Hardy space, RBMO space, boundedness, non-doubling measure