Abstract
We prove the boundedness of a class of pseudo-differential operators on the Hörmander spaces \({\dot H^{0,p}},1 < p < \infty .\) Examples are given to show that the classical pseudo-differential operators fail to be bounded on these spaces. Fourier integral operators and their global mapping properties are studied in this setting. Applications to the regularity of solutions of semilinear pseudo-differential equations on ℝn are presented.
This is an expanded version of a lecture given at the ISAAC97 Conference, University of Delaware, June 3–7, 1997.
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Iancu, G.M. (2000). Boundedness of Pseudo-Differential Operators on Hörmander Spaces. In: Gilbert, R.P., Kajiwara, J., Xu, Y.S. (eds) Direct and Inverse Problems of Mathematical Physics. International Society for Analysis, Applications and Computation, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3214-6_7
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DOI: https://doi.org/10.1007/978-1-4757-3214-6_7
Publisher Name: Springer, Boston, MA
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