Notation for asymptotic bounds on both sides I am writing my first paper, and one of the results can be written as follows:


  For any $W,\epsilon$ such that $\epsilon = o\left(\frac{\log^4 W}{W\log\log W}\right)$ and $\epsilon=\omega\left(\frac{\log\log W}{W}\right)$, we obtain a $o(\min \{W, \frac{1}{\epsilon}{\log^2 W}\})$ space algorithm, improving the state of the art.


Is there some standard notation, say $\Gamma$, so I could write:


  For any $W$ and $\epsilon=\Gamma\left(\frac{\log\log W}{W}, \frac{\log^4 W}{W\log\log W}\right)$, ...


?

Will appreciate any help !
I'm also not aware of any specific notation for the concept you want. In the example theorem statement in the question, there's nothing wrong with what you already have ("$\epsilon$ such that $\epsilon=o(\cdots)$ and $\epsilon=\omega(\cdots)$"). In other situations, it might be more convenient to say something like, "For any $\epsilon\in o(\cdots)\cap\omega(\cdots)$".