Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On persistence properties in fractional weighted spaces   In this work we derive a point-wise formula that will allows us to study the
well-posedness of initial value problem associated to nonlinear dispersive
equations in fractional weighted Sobolev spaces $H^s(\R)\cap L^2(|x|^{2r}dx)$,
$s, r \in \R$. As an application of this formula we will study local and global
well posedness of the $k$-generalized Korteweg-de Vries equation in these
weighted Sobolev spaces.

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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int