Reaction between hydrogen peroxide and ozone
This is basically an excerpt of the answer I have given to another quite similar question.

Ben is quite right, neither the reaction nor the mechanism is simple. It involves several different radical chains all resulting in the decomposition of ozone.[a]

It is most likely that the reaction will start with the formation of oxygen radicals in the gas phase ($\ce{O}$ atom transfer).$$\ce{O3 + O3 -&gt; O3 + O2 + O}$$

In presence of Hydrogen donors like $\ce{H2O2}$, which "is expected to be an excellent $\ce{H}$ donor."[a] Those are forming the main chain carriers will be $\ce{HO, HO2}$.
 Finally stopping at some point by recombination of these species.
\begin{aligned}\ce{
O + H2O2 &amp;-&gt; OH + HO2\\
  HO + O3 &amp;-&gt; HO2 + O2\\
  HO2 + O3 &amp;-&gt; HO + 2O2\\
  2HO2 &amp;-&gt;}\text{stable products}
\end{aligned}

In aqueous solution the decomposition is highly pH dependent, but may always work because of autoprotolysis. $$\ce{2H2O &lt;=&gt; H3+O + {}^{-}OH}$$

Especially important might also be protolysis of hydrogen peroxide. $$\ce{H2O2 + H2O &lt;=&gt; HO2- + H3+O}$$

Steahelin and Hoigné propose several hypotheses in which way ozone will be decomposed, but I will not go into absurd detail here.[b] The core assumptions involve $\ce{{}^{-}OH}$ as the initiator of a radical chain. Followed by radical (ionic) species like $\ce{.O2-, .O3-, HO2., .OH}$ resulting again in a chain reaction. 
\begin{aligned}\ce{
  O3 + {}^{-}OH &amp;-&gt; .O2- + HO2.\\  
  O3 + {}^{-}OH &amp;-&gt; HO2- + O2\\ 
  O3 + {}^{-}OH &amp;-&gt; .O3- + .OH\\
  HO2. &amp;&lt;=&gt; H+ + .O2-\\
  O3 + HO2- &amp;-&gt; .OH + .O2- + O2\\
  O3 + .O2- &amp;-&gt; .O3- + O2\\
  .O3- + H2O &amp;-&gt; .OH + {}^{-}OH + O2
}\end{aligned}