Extending BMO functions in parabolic setting

Abstract

We prove that one can extend any $BM{O}^x$ function $a$ given in a cube in ${\mathbb{R}}^{d+1}$ to become a $BM{O}^x$ functions $\hat{a}$ in ${\mathbb{R}}^{d+1}$ almost preserving its $[a{]}^{♯}$ seminorm, which is, loosely speaking, $L_{\infty }$-norm of the maximal function in $t$ and $BMO$-norm in $x$.

7 pages