Energy conditions and twisted localizations of operators

Published 11 Jan 2018 in math.CA | (1801.03706v2)

Abstract: 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.

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Eric T. Sawyer

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