Abstract
Pseudo-differential operators with coefficients in Sobolev spaces H r , q , 1 ⩽ q ⩽ ∞ {H^{r,q}},1 \leqslant q \leqslant \infty , and their adjoints are studied on Hardy-Sobolev spaces H s , p , 0 > p ⩽ ∞ {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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