Pointwise multipliers on martingale Campanato spaces

Abstract

We introduce generalized Campanato spaces ${\mathcal{L}}_{p,\varphi }$ on a probability space $(\Omega ,\mathcal{F},P)$, where $p\in [1,\infty )$ and $\varphi :(0,1]\to (0,\infty )$. If $p=1$ and $\varphi \equiv 1$, then ${\mathcal{L}}_{p,\varphi }=\mathrm{BMO}$. We give a characterization of the set of all pointwise multipliers on ${\mathcal{L}}_{p,\varphi }$.

18 pages, Studia Mathematica (to appear)