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Brief communications

On boundedness of pseudodifferential operators in Hölder–Zygmund spaces with variable order of smoothness

G. P. Omarova

Institute of Mathematics, Mechanics and Computer Science, Southern Federal University, 8a Milchakov str., Rostov-on-Don, 344090 Russia

Abstract: We consider the Hölder–Zygmund spaces of functions with variable index of smoothness defined on finite-dimensional real space. The index of smoothness depends on a point in this space and may take negative values. We prove the boundedness theorem for pseudodifferential operators with exotic symbols the from Hörmander classes in these spaces.

Keywords: pseudodifferential operators, Hölder–Zygmund spaces, variable index of smoothness.

UDC: 517.983

Presented by the member of Editorial Board: S. G. Samko
Received: 27.11.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:6, 68–70

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