Bilinear pseudodifferential operators with symbol in BS_{1,1}^m on Triebel–Lizorkin spaces with critical Sobolev index

• Arias, Sergi ^[1] ; Rodríguez-López, Salvador ^[1]
  1. [1] Stockholm University

     Stockholm University

     Suecia

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 2, 2024, págs. 567-591
• Idioma: inglés
• DOI: 10.1007/s13348-023-00400-0
• Enlaces
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• Resumen

  • In this paper we obtain new estimates for bilinear pseudodifferential operators with symbol in the class BS_{1,1}^m, when both arguments belong to Triebel-Lizorkin spaces of the type F_{p,q}^{n/p}({\mathbb {R}}^n). The inequalities are obtained as a consequence of a refinement of the classical Sobolev embedding F^{n/p}_{p,q}({\mathbb {R}}^n)\hookrightarrow \textrm{bmo}({\mathbb {R}}^n) , where we replace \textrm{bmo}({\mathbb {R}}^n) by an appropriate subspace which contains L^\infty ({\mathbb {R}}^n). As an application, we study the product of functions on F_{p,q}^{n/p}({\mathbb {R}}^n) when 1p \infty, where those spaces fail to be multiplicative algebras.

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