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I'm looking for articles describing (or proving nonexistence) of isometric embeddings of $m$-dimensional space $\ell_q^m$ into $L_p$ and $\ell_p$ for $q,p\in[1,+\infty]$.

Since $\ell_q^m$ is finite dimensional some (not necessary isometric) embedding always exist. I'm interested in isometric ones.

Thank you for taking time.

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    It's not exactly addressing your question, but did you see [this blog post](http://calculus7.org/2012/08/07/isometric-embeddings-of-finite-dimensional-normed-spaces/) by Leonid Kovalev? He recommends the book by [Milman and Schechtman](http://books.google.com/books/about/Asymptotic_Theory_of_Finite_Dimensional.html?id=tTnvAAAAMAAJ) for the "real stuff".2012-10-29
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    what does "real stuff" mean?2012-10-29
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    I'm only quoting him. I suppose he means that the sharpest known embedding constants between finite-dimensional $\ell_p$-spaces and much more can be found there. I don't know the book, but given the reputation of its authors it's probably worth a look. // You said elsewhere that you were reading the book by Albiac-Kalton. The chapter on local theory should contain something, too.2012-10-29
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    @commenter Yes using result on embedding of $\ell_q$ in $L_p$ we can get some partial progress. The case $p=\infty$ is also of small interest because every separeable space ismotrically embedded in $\ell_\infty$ and $L_\infty$.2012-10-29
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    @commenter I've got an answer on MO, see my answer below.2012-10-30
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    Thanks, Bill Johnson to the rescue :)2012-10-30
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    @commenter As usually, he is just awesome :)2012-10-30

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Here is an answer to this question on mathoverflow.