A probabilistic approach to 𝐻^{𝑝}(𝑅^{𝑑})

Abstract

The relationship between H p ( R d ) , 1 ≤ p > ∞ {H^p}({R^d}),1 \leq p > \infty , and the integrability of certain functionals of Brownian motion is established using the connection between probabilistic and analytic notions of functions with bounded mean oscillation. An application of this relationship is given in the derivation of an interpolation theorem for operators taking H 1 ( R d ) {H^1}({R^d}) to L 1 ( R d ) {L^1}({R^d}) .