TY - JOUR
T1 - Non existence of principal values of signed riesz transforms of non integer dimension
AU - Ruiz De Villa, Aleix
AU - Tolsa, Xavier
PY - 2010/7/20
Y1 - 2010/7/20
N2 - In this paper we prove that, given s ≥ 0, and a Borel non zero measure μ in Rm, if for μ-almost every x ∈ Rm the limit mathematical equation presented exists and 0 < lim sup r→0μ(B(x; r)) /rs < ∞, then s in an integer. In particular, if E ⊂ Rm is a set with positive and bounded s-dimensional Hausdorff measure Hs and for H s-almost every x ∈ E the limit mathematical equation presented exists, then s is an integer. ©, Vol. 59, No. 1 (2010).
AB - In this paper we prove that, given s ≥ 0, and a Borel non zero measure μ in Rm, if for μ-almost every x ∈ Rm the limit mathematical equation presented exists and 0 < lim sup r→0μ(B(x; r)) /rs < ∞, then s in an integer. In particular, if E ⊂ Rm is a set with positive and bounded s-dimensional Hausdorff measure Hs and for H s-almost every x ∈ E the limit mathematical equation presented exists, then s is an integer. ©, Vol. 59, No. 1 (2010).
KW - Hausdorff measures
KW - Riesz transforms
UR - https://dialnet.unirioja.es/servlet/articulo?codigo=3224613
U2 - 10.1512/iumj.2010.59.3884
DO - 10.1512/iumj.2010.59.3884
M3 - Article
SN - 0022-2518
VL - 59
SP - 115
EP - 130
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
ER -