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arXiv · 1609.07945

$L_p$-Theory of Type $1,1$-Operators

Jon Johnsen
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Abstract

This is a continuation of recent work on the general definition of pseudo-differential operators of type $1,1$, in Hörmander's sense. Continuity in $L_p$-Sobolev spaces and Hölder--Zygmund spaces, and more generally in Besov and Lizorkin--Triebel spaces, is proved for positive smoothness, with extension to arbitrary smoothness for operators in the self-adjoint subclass. As a main tool the paradifferential decomposition is used for type $1,1$-operators in combination with the Spectral Support Rule for pseudo-differential operators and pointwise estimates in terms of maximal functions of Peetre--Fefferman--Stein type.

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Jon Johnsen. 2016-09-26. $L_p$-Theory of Type $1,1$-Operators. https://doi.org/10.1002/mana.201100179

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