TY - JOUR
T1 - A Method of Rotations for Lévy multipliers
AU - Perlmutter, Michael
N1 - We use a method of rotations to study the $$L^p$$ L p boundedness, for $$1<p<\infty $$ 1 < p < ∞ , of Fourier multipliers which arise as the projection of martingale transforms with respect to symmetric $$\alpha $$ α -stable processes, $$0<\alpha <2$$ 0 < α < 2 .
PY - 2017/12
Y1 - 2017/12
N2 - We use a method of rotations to study the Lp boundedness, for 1 < p < ∞, of Fourier multipliers which arise as the projection of martingale transforms with respect to symmetric α -stable processes, 0 < α < 2. Our proof does not use the fact that 0 < α < 2, and therefore allows us to obtain a larger class of multipliers which are bounded on Lp . As in the case of the multipliers which arise as the projection of martingale transforms, these new multipliers also have potential applications to the study of the Lp boundedness of the Beurling-Ahlfors transform.
AB - We use a method of rotations to study the Lp boundedness, for 1 < p < ∞, of Fourier multipliers which arise as the projection of martingale transforms with respect to symmetric α -stable processes, 0 < α < 2. Our proof does not use the fact that 0 < α < 2, and therefore allows us to obtain a larger class of multipliers which are bounded on Lp . As in the case of the multipliers which arise as the projection of martingale transforms, these new multipliers also have potential applications to the study of the Lp boundedness of the Beurling-Ahlfors transform.
KW - Beurling–Ahlfors transform
KW - Fourier multipliers
KW - Lévy processes
KW - martingale transforms
KW - method of rotations
UR - https://doi.org/10.1007/s00209-017-1845-8
U2 - 10.1007/s00209-017-1845-8
DO - 10.1007/s00209-017-1845-8
M3 - Article
VL - 287
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3-4
ER -