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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Pseudodifferential operators with coefficients in Sobolev spaces


Author: Jürgen Marschall
Journal: Trans. Amer. Math. Soc. 307 (1988), 335-361
MSC: Primary 35S05; Secondary 35A27, 47G05
MathSciNet review: 936820
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Abstract: Pseudo-differential operators with coefficients in Sobolev spaces $ {H^{r,q}},1 \leqslant q \leqslant \infty $, and their adjoints are studied on Hardy-Sobolev spaces $ {H^{s,p}},\;0 < p \leqslant \infty $. A symbolic calculus for these operators is developed, and the microlocal properties are studied. Finally, the invariance under coordinate transformations is proved.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0936820-3
PII: S 0002-9947(1988)0936820-3
Keywords: Pseudo-differential operators, nonregular symbols, Sobolev spaces, microlocal analysis
Article copyright: © Copyright 1988 American Mathematical Society