Paper on mathematical analysis using tools from other (almost unrelated) field: how to introduce them?

Question

I'm a PhD student working in Stochastic calculus/Malliavin calculus, and I am currently writing a paper (my second one), in which I use tools from probability theory to solve an Analysis problem. My idea was to write it in such a way that not only a probabilist could read it, but also an analyst (since the problem I "solve" has more relevance when considered from the Analysis perspective).

In order to achieve this I had to write an first section with preliminary results where I tried to "translate" some of the concepts/tools into a more "analyst-friendly" language since I am not sure if the general public working in mathematical analysis has some familiarity with Malliavin/Hida-calculus.

The problem is that even though I need only a few lemmas from Malliavin/Hida-calculus, in order to prove those I've ended up with a 15-pages-long "introductory" section, while the statement & proof of my result can be written in at most 3 pages.

This seems somehow "unbalanced", what do you think? Is it always necessary to provide a proof for the "intermediate lemmas", or maybe I could write something like "the interested reader in refer to ...". If this was a paper for people working in the field I would certainly ommit some.

I know this is something I could discuss with my supervisor, but he is a probabilist and I would like to listen the opinion of some analyst.

Thanks in advance!

Answer 1

An appendix, maybe

In many other fields it is typical to first choose a journal and only then start writing. In mathematics this is often not done. But here it might be relevant to consider your target audience and thereby target journal.

If the problem is from analysis and you want to publish it in a journal devoted to analysis (or in any non-stochastics journal), an appendix with the stochastics might be appropriate. In any case, formatting the paper so that it can be read without the material in the appendix is a worthwhile task. It also makes it simple to react to referee comments concerning the usefulness of the appendix, if you get such: you can keep it, integrate it back into the main text or remove it with only a little trouble.

If you think the paper is of (more) interest to people into Malliavin calculus, or would be easier to publish in a journal close to stochastics, then maybe leaving out the basics is desirable. But remember to motivate the problem sufficiently.