Proceedings of the Centre for Mathematics and its Applications

Riesz transforms of some parabolic operators

E. M. Ouhabaz and C. Spina

Full-text: Open access

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 $f \in L^p([0,T] \times \mathbb{R}^N)$.

Article information

Source
AMSI International Conference on Harmonic Analysis and Applications. Xuan Duong, Jeff Hogan, Chris Meaney, and Adam Sikora, eds. Proceedings of the Centre for Mathematics and its Applications, v. 45. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 2013), 115-123

Dates
First available in Project Euclid: 3 December 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1417630508

Mathematical Reviews number (MathSciNet)
MR3424870

Zentralblatt MATH identifier
1338.42028

Citation

Ouhabaz, E. M.; Spina, C. Riesz transforms of some parabolic operators. AMSI International Conference on Harmonic Analysis and Applications, 115--123, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 2013. https://projecteuclid.org/euclid.pcma/1417630508


Export citation