It's considered very bad form in HTML to have the scope of tags overlap at all. Something of the form <p><i>...</p>...</i> should never exist. Probably it would mean that the HTML in question wouldn't pass validation tests.
So if you have multiple italicized paragraphs, you should have something like:
<p><i>Paragraph one ..</i></p>
<p><i>Paragraph two ..</i></p>
or better:
<p style="font-style: italic;">Paragraph one</p>
<p style="font-style: italic;>Paragraph two</p>
(Or the same by means of a CSS class and an appropriate stylesheet.)
Something like:
<div style="font-style: italic;">
<p>Paragraph one</p>
<p>Paragraph two</p>
</div>
might be OK, but it might have other issues, so I'd steer clear of it.