Abstract
In this chapter we present a brief description of the basic concepts and results of the Lp theory of pseudo-differential operators which may be considered as a modern theory of the classical potential theory. In particular, we formulate the Besov space boundedness theorem due to Bourdaud [Bo] (Theorem 3.15) and a useful criterion for hypoellipticity due to Hörmander [Ho2] (Theorem 3.16) which play an essential role in the proof of our main results. For detailed studies of pseudo-differential operators, the reader is referred to Chazarain–Piriou [CP], Hörmander [Ho3], Kumano-go [Ku] and Taylor [Ty].
Keywords
- Open Subset
- Phase Function
- Besov Space
- Continuous Linear Operator
- Fourier Integral Operator
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© 2009 Springer-Verlag Berlin Heidelberg
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Taira, K. (2009). Lp Theory of Pseudo-Differential Operators. In: Boundary Value Problems and Markov Processes. Lecture Notes in Mathematics(), vol 1499. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01677-6_3
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DOI: https://doi.org/10.1007/978-3-642-01677-6_3
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01676-9
Online ISBN: 978-3-642-01677-6
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