Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudodifferential operators with rough symbols   In this work, we develop $L^p$ boundedness theory for pseudodifferential
operators with rough (not even continuous in general) symbols in the $x$
variable. Moreover, the $B(L^p)$ operator norms are estimated explicitly in
terms of scale invariant quantities involving the symbols. All the estimates
are shown to be sharp with respect to the required smoothness in the $\xi$
variable. As a corollary, we obtain $L^p$ bounds for (smoothed out versions of)
the maximal directional Hilbert transform and the Carleson operator.

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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin