Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy conditions and twisted localizations of operators   We show that the energy conditions are not necessary for boundedness of
fractional Riesz transforms in dimension at least 2. We also give a weak
converse, namely that the energy conditions are necessary for boundedness of
families of twisted localizations of fractional singular integrals having the
positive gradient property.

33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
22
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: atom-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th