Continuity and compactness for pseudo-differential operators with symbols in quasi-Banach spaces or Hörmander classes

2017 ◽  
Vol 15 (03) ◽  
pp. 353-389 ◽  
Author(s):  
Joachim Toft
Keyword(s):  
Banach Spaces ◽  
Differential Operators ◽  
Modulation Spaces ◽  
Von Neumann ◽  
Norm Estimates ◽  
Pseudo Differential Operators

We deduce continuity and Schatten–von Neumann properties for operators with matrices satisfying mixed quasi-norm estimates with Lebesgue and Schatten parameters in [Formula: see text]. We use these results to deduce continuity and Schatten–von Neumann properties for pseudo-differential operators with symbols in quasi-Banach modulation spaces, or in appropriate Hörmander classes.

scholarly journals Operator Symbols and Operator Indices

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 64
Author(s):  
Vladimir Vasilyev
Keyword(s):  
Banach Spaces ◽  
Differential Operators ◽  
Index Theorem ◽  
Symbolic Calculus ◽  
Smooth Manifolds ◽  
Bounded Operators ◽  
Pseudo Differential Operators ◽  
Operator Symbols ◽  
Special Classes

We suggest a certain variant of symbolic calculus for special classes of linear bounded operators acting in Banach spaces. According to the calculus we formulate an index theorem and give applications to elliptic pseudo-differential operators on smooth manifolds with non-smooth boundaries.

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