L2-boundedness of the SIO with kernel K_4 on 1-Ahlfors regular sets in the Heisenberg group characterizes containment in 1-Ahlfors regular curves, with negative results for alpha in (0,2) and a bounded operator on a purely 1-unrectifiable set.
Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI
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On singular integrals with non-negative kernels in the Heisenberg group
L2-boundedness of the SIO with kernel K_4 on 1-Ahlfors regular sets in the Heisenberg group characterizes containment in 1-Ahlfors regular curves, with negative results for alpha in (0,2) and a bounded operator on a purely 1-unrectifiable set.