On the boundedness of semiclassical pseudodifferential operators on Triebel-Lizorkin spaces

Document Type : Original Article

Authors

Omar Farouk Aid ¹

Chahrazed Harrat ²

Abderrahmane Senoussaoui ¹

¹ Laboratory of Fundamental and Applied Mathematics‎ ‎of Oran (LMFAO)‎, ‎University of Oran 1‎, ‎Ahmed Ben Bella‎. ‎B.P‎. ‎1524 El‎ ‎M'naouar‎, ‎Oran‎, ‎Algeria

² Department of Mathematics‎, ‎Faculty of Mathematics and‎ ‎Computer Sciences‎, ‎University of Sciences and Technology‎ ‎"M.B"‎ ‎of‎ ‎Oran‎, ‎Algeria

10.22034/kjm.2024.459109.3212

Abstract

‎In this paper‎, ‎we study a specific class of $h$-pseudo-differential‎ operators with H\"{o}rmander's symbol‎. ‎This class of operators can‎ be extended as a bounded linear mapping on Triebel--Lizorkin spaces‎.

Keywords

Pseudodifferential operators

Hardy-Littlewood maximal operator

Triebel-Lizorkin spaces

Subjects

• 35 Partial differential equations

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