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A CHARACTERIZATION OF FREDHOLM PSEUDO-DIFFERENTIAL OPERATORS

Published online by Cambridge University Press:  01 February 1997

QIHONG FAN  and
M. W. WONG
QIHONG FAN
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, People's Republic of China
M. W. WONG
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3
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Abstract

We give a necessary and sufficient condition on an elliptic symbol σ of order m to ensure that the unique closed extension in Lp(ℝn) for 1 < p < ∞, of the pseudo-differential operator Tσ, initially defined on the Schwartz space, is a Fredholm operator from Lp(ℝn) into Lp(ℝn) with domain Hm, p, where Hm, p is the Lp Sobolev space of order m.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 55 , Issue 1 , February 1997 , pp. 139 - 145
Copyright
The London Mathematical Society 1997

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