TY - JOUR
T1 - NON-EXISTENCE OF REFLECTIONLESS MEASURES FOR THE s-RIESZ TRANSFORM WHEN 0 < s < 1
AU - Prat, Laura
AU - Tolsa, Xavier
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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.
AB - 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.
KW - rectifiability
KW - reflectionless measure
KW - Riesz transforms
KW - Wolff potential
UR - https://www.scopus.com/pages/publications/85044751753
U2 - 10.5186/aasfm.2015.4055
DO - 10.5186/aasfm.2015.4055
M3 - Article
AN - SCOPUS:85044751753
SN - 1239-629X
VL - 40
SP - 957
EP - 968
JO - Annales Academiae Scientiarum Fennicae Mathematica
JF - Annales Academiae Scientiarum Fennicae Mathematica
ER -