I am looking for the following version of Calderon-Zygmund decomposition, consider an function $f \in L^1(R^{d+1})$ and cylinders of the form $Q_{R,R^p}$ for some fixed $p \in (0,\infty)$, The cylinders are cubes of radius $R$ in $R^d$ and of height $R^p$ in the time direction.

Question: Can I find a sequence of cubes $\{Q_i\}$ such that Calderon Zygmund decomposition holds and each cube $\{Q_i\}$ has scaling of the form $(r,r^p)$?