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

Abstract

Fractional Sobolev spaces ${\hat{H}}^s(\mathbb{R})$ 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.

arXiv admin note: text overlap with arXiv:1807.01847