Oblivious Turing Machine emulation lower bound Is there a proof that the emulation of a Turing machine on an oblivious Turing machine can't be done in less than $\mathcal{O}\left(m\log m\right)$ where $m$ is the number of steps the Turing machine uses? Or is this just an upper bound?

In the paper of Paul Vitányi about relativized oblivious Turing machines, Vitányi claims


  "They [Pippenger and Fischer, 1979] showed that this result cannot be improved in general, since there is a language L wich is recognized by a 1-tape real-time Turing machine $M$, and any oblivious Turing machine $M'$ recognizing $L$ must use at least an order $O(n \log n)$ steps".


This should state $O(m \log m)$ as an absolute bound. However I don't find any proof of this in 

Pippenger, Nicholas; Fischer, Michael J., Relations among complexity measures, J. Assoc. Comput. Mach. 26, 361-381 (1979). ZBL0405.68041.

Any ideas?
Furthermore, what is the space complexity of this emulation? As far as I know the conversion to a universal Turing machine only doubles the tape length. Can I assume that the space complexity is $\mathcal{O}\left(l\right)$ with $l$ the space complexity of the original Turing machine?
As mentioned above, it is not known in general if there is a faster oblivious simulation.

But interesting lower bounds for this problem are known, under more constrained conditions. For instance, what if you want an oblivious simulation that preserves not only the time $t$ but also the space usage $s$? Beame and Machmouchi have recently proved an interesting time-space tradeoff lower bound for this problem: either the space must increase by a factor of $n^{1-o(1)}$, or the time must increase by a factor of $\Omega(\log n \cdot \log \log n)$.

The paper is here: http://eccc.hpi-web.de/report/2010/104/