arXiv subjects

Michael Perlmutter

Publications and source records attributed to Michael Perlmutter.

38 records · Page 3Linked to original sources

arXiv2015

A Method of Rotations for Lévy Multipliers

We use a method of rotations to study the $L^p$ boundedness, $1<p<\infty$, 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 $L^p$. 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 $L^p$ boundedness of the Beurling-Ahlfors transform.

math.PR↗

arXiv2013

On a class of Calderón-Zygmund operators arising from projections of martingale transforms

We prove that a large class of operators, which arise as the projections of martingale transforms of stochastic integrals with respect to Brownian motion, as well as other closely related operators, are in fact Calderón--Zygmund operators. Consequently, such operators are not only bounded on $L^p$, $1<p<\infty$, but also satisfy weak-type inequalities. Unlike the boundedness on $L^p,$ which can be obtained directly from the Burkholder martingale transform inequalities, the weak-type estimates do not follow from the corresponding martingale results.

math.PR↗