The point-wise product of a function of bounded mean oscillation with a function of the Hardy space $H^1$ is not locally integrable in general. However, in view of the duality between $H^1$ and $BMO$, we are able to give a meaning to the product as a Schwartz distribution. Moreover, this distribution can be written as the sum of an integrable function and a distribution in some adapted Hardy-Orlicz space. When dealing with holomorphic functions in the unit disc, the converse is also valid: every holomorphic...

The paper establishes integral representation formulas in arbitrarily wide Banach spaces $b_{\omega }^p\left({ℝ}^n\right)$ of functions harmonic in the whole ${ℝ}^n$.