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Pseudo-Differential Operators in Hölder Spaces Revisited: Weyl–Hörmander Calculus and Ruzhansky–Turunen Classes

  • Duván CardonaEmail author
Article
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Abstract

In this work, we obtain continuity results on Hölder spaces for operators belonging to a Weyl–Hörmander calculus for metrics such that the class of the associated operators contains, in particular, certain hypoelliptic laplacians. With our results we recover some historical Hölder boundedness theorems (see Beals in Annales de l’institut Fourier 29(3):239–260, 1979; Lp and Holder estimates for pseudodifferential operators: necessary conditions. In: Harmonic analysis in Euclidean spaces (proceedings of symposia in pure mathematics, Williams College, Williamstown, MA, 1978). American Mathematical Society, Providence, pp 153–157, 1979). The action of (periodic) Ruzhansky–Turunen classes of pseudo-differential operators on Hölder spaces also will be investigated.

Keywords

Pseudo-differential operators on \(R^n\) Toroidal pseudo-differential operators Weyl–Hörmander calculus Ruzhansky–Turunen classes Hölder spaces 

Mathematics Subject Classification

Primary 35J70 Secondary 35A27 47G30 

Notes

Acknowledgements

The author wants to express his gratitude to the referee who pointed out a number of suggestions helping to improve the presentation of the manuscript.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsPontificia Universidad JaverianaBogotáColombia

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