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VOL. 45 | 2013 Riesz transforms of some parabolic operators
E. M. Ouhabaz, C. Spina

Editor(s) Xuan Duong, Jeff Hogan, Chris Meaney, Adam Sikora

Abstract

We study boundedness on $L^p([0,T]) \times \mathbb{R}^N$ of Riesz transforms $\nabla(\mathcal{A})^{-1/2}$ for class of parabolic operators such as $A = \frac{\partial}{\partial t} - \Delta + V(t,x)$. Here $V(t,x)$ is a non-negative potential depending on time ${t}$ and space variable ${x}$. As a consequence, we obtain $W_{x}^{1,p}$-solutions for the non-homogeneous problem \[ \partial_{t}u - \Delta u + V(t,.)u = f(t,i), u(0) = 0 \] for initial data $f \in L^p([0,T] \times \mathbb{R}^N)$.

Information

Published: 1 January 2013
First available in Project Euclid: 3 December 2014

zbMATH: 1338.42028
MathSciNet: MR3424870

Rights: Copyright © 2013, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.

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