Characterizations of Fractional Sobolev Spaces From the Perspective of Riemann-Liouville Operators

2018/09/02 by Yulong Li, Li, Yulong
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1809.00398

openalex publication_date 2018/09/02 · openalex created_date 2018/09/27 · openalex updated_date 2026/07/28

Abstract

Fractional Sobolev spaces \widehatH^s(ℝ) have been playing important roles in analysis of many mathematical subjects. In this work, we re-consider fractional Sobolev spaces under the perspective of fractional operators and establish characterizations on the Fourier transform of functions of fractional Sobolev spaces, thereby giving another equivalent definition.

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