On the product of functions in $BMO$ and $H^1$ over spaces of homogeneous type

Luong Dang Ky (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

Let $\mathcal X$ be an RD-space, which means that $\mathcal X$ is a space of homogeneous type in the sense of Coifman-Weiss with the additional property that a reverse doubling property holds in $\mathcal X$. The aim of the present paper is to study the product of functions in $BMO$ and $H^1$ in this setting. Our results generalize some recent results in \cite{Feu} and \cite{LP}.

Mots clés: Musielak-Orlicz function; Hardy space; BMO; space of homogeneous type; admissible function; atomic decomposition; maximal function

Domaines: Analyse classique [math.CA]

Luong Dang Ky. On the product of functions in $BMO$ and $H^1$ over spaces of homogeneous type. Journal of Mathematical Analysis and Applications, 2015, 11 p. ⟨hal-01053890⟩