Paradifferential Operators

  • Michael E. Taylor
Part of the Progress in Mathematics book series (PM, volume 100)


The key tool of paradifferential operator calculus is developed in this chapter, beginning with Meyer’s ingenious formula for F(u) as M(x, D)u + R where F is smooth in its argument (s), u belongs to a Hölder or Sobolev space, M(x, D) is a pseudodifferential operator of type 1,1, and R is smooth. From there, one applies symbol smoothing to M(x, ξ) and makes use of results established in Chapter 2. The tool that arises is quite powerful in nonlinear analysis. The first glimpse we give of this is that it automatically encompasses some important Moser estimates. We re-derive elliptic regularity results established in Chapter 2, after establishing some microlocal regularity results. In §3.3 we do this using symbol smoothing with δ < 1; in §3.4 we present some results of Bony and Meyer dealing with the δ = 1 case, the case of genuine paradifferential operators.


Differential Operator Pseudodifferential Operator Pseudo Differential Operator Regularity Result Para Differential Operator 
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Michael E. Taylor
    • 1
  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA

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