Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The H\"ormander Multiplier Theorem III: The complete bilinear case via
  interpolation   We develop a special multilinear complex interpolation theorem that allows us
to prove an optimal version of the bilinear H\"ormander multiplier theorem
concerning symbols that lie in the Sobolev space $L^r_s(\mathbb R^{2n})$, $2\le
r<\infty$, $rs>2n$, uniformly over all annuli. More precisely, given a
smoothness index $s$, we find the largest open set of indices $(1/p_1,1/p_2 )$
for which we have boundedness for the associated bilinear multiplier operator
from $L^{p_1}(\mathbb R^{ n})\times L^{p_2} (\mathbb R^{ n})$ to $ L^p(\mathbb
R^{ n})$ when $1/p=1/p_1+1/p_2$, $1<p_1,p_2<\infty$.

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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg