Bilinear pseudodifferential operators with symbol in BS_1,1^m on Triebel-Lizorkin spaces with critical Sobolev index

2022/12/07 by Sergi Arias, Salvador Rodríguez-López, Arias, Sergi +1
Mathematics · #46E35 #47G30 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2212.03542

openalex publication_date 2022/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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(ℝⁿ). The inequalities are obtained as a consequence of a refinement of the classical Sobolev embedding F^n/p_p,q(ℝⁿ)\hookrightarrowbmo(ℝⁿ), where we replace bmo(ℝⁿ) by an appropriate subspace which contains L^∞(ℝⁿ). As an application, we study the product of functions on F_p,q^n/p(ℝⁿ) when 1

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