Abstract
We prove a Melin-Hörmander inequality for a Banach algebra of pseudo-differential operators whose calculus was developed by Sjöstrand. The main new difficulties in the proof are settled by a stationary phase method tailored to the low-regularity of the symbols.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bony, J.-M. andLerner, N., Quantification asymptotique et microlocalisations d’ordre supérieur I,Ann. Sci. École Norm. Sup. 22 (1989), 377–433.
Boulkhemair, A.,L 2 estimates for pseudodifferential operators,Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 (1995), 153–183.
Boulkhemair, A., Remarks on a Wiener type pseudodifferential algebra and Fourier integral operators,Math. Res. Lett. 4 (1997), 53–67.
Coifman, R. andMeyer, Y.,Au delà des opérateurs pseudo-différentiels, Astérisque57, Soc. Math. France, Paris, 1978.
Hörmander, L., The Weyl calculus of pseudodifferential operators,Comm. Pure Appl. Math. 32 (1979), 360–444.
Melin, A., Lower bounds for pseudo-differential operators,Ark. Mat. 9 (1971), 117–140.
Sjöstrand, J., An algebra of pseudodifferential operators,Math. Res. Lett. 1 (1994), 185–192.
Sjöstrand, J., Wiener type algebras of pseudodifferential operators, inSéminaire sur les Équations aux Dérivées Partielles, 1994–1995, Exp.IV, Ecole Polytech., Palaiseau, 1995.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hérau, F. Melin-Hörmander inequality in a Wiener type pseudo-differential algebra. Ark. Mat. 39, 311–338 (2001). https://doi.org/10.1007/BF02384559
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02384559