A remark on a paper of F. Chiarenza and M. Frasca

2023/10/10 by Н. В. Крылов, Krylov, N. V. · 1 citation
Computer Science · Mathematics · #42B25 #46E35 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2310.12170

openalex publication_date 2023/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1990 F. Chiarenza and M. Frasca published a paper in which they generalized a result of C. Fefferman on estimates of the integral of |bu|^p through the integral of |Du|^p for p>1. Formally their proof is valid only for d≥ 3. We present here further generalization with a different proof in which D is replaced with the fractional power of the Laplacian for any dimension d≥ 1.

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