A measure μ on Rd is called reflectionless for the s-Riesz transform if the singular integral (Formula presented) is constant on the support of μ in some weak sense and, moreover, the operator defined by (Formula presented) is bounded in L2(μ). In this paper we show that the only reflectionless measure for the s-Riesz transform is the zero measure when 0 < s < 1.
|Number of pages||12|
|Journal||Annales Academiae Scientiarum Fennicae Mathematica|
|Publication status||Published - 1 Jan 2015|
- reflectionless measure
- Riesz transforms
- Wolff potential