Criteria for the compactness and the Fredholm property of pseudodifferential operators in Hölder-Zygmund weighted spaces

Author: Kryakvin V.  

Publisher: MAIK Nauka/Interperiodica

ISSN: 0012-2661

Source: Differential Equations, Vol.45, Iss.1, 2009-01, pp. : 102-112

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Abstract

We obtain necessary and sufficient conditions for the complete continuity (the Fredholm property) in Hölder-Zygmund spaces on ℜ n whose weight has a power-law behavior at infinity for pseudodifferential operators with symbols in the Hörmander class S 1,δ m , 0 ≤ δ < 1 (slowly varying symbols in the class S 1,0 m ). We show that such operators are compact operators or Fredholm operators in weighted Hölder-Zygmund spaces if and only if they are compact operators or Fredholm operators, respectively, in Sobolev spaces.