The fractional Bessel equation in Hölder spaces

Abstract

Motivated by the Poisson equation for the fractional Laplacian on the whole space with radial right hand side, we study global Hölder and Schauder estimates for a fractional Bessel equation. Our methods stand on the so-called semigroup language. Indeed, by using the solution to the Bessel heat equation we derive pointwise formulas for the fractional operators. Appropriate Hölder spaces, which can be seen as Campanato-type spaces, are characterized through Bessel harmonic extensions and fractional Carleson measures. From here the regularity estimates for the fractional Bessel equations follow. In particular, we obtain regularity estimates for radial solutions to the fractional Laplacian.

36 pages. To appear in Journal of Approximation Theory

References in corpus (2)

• Square functions in the Hermite setting for functions with values in UMD spaces
• Vector valued multivariate spectral multipliers, Littlewood-Paley functions, and Sobolev spaces in hte Hermite setting

Cited by in corpus (5)

• Fractional Sobolev Spaces for the Singular-perturbed Laplace Operator in the $L^p$ setting
• UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces
• Subordinated Bessel heat kernels
• BMO functions and Balayage of Carleson measures in the Bessel setting
• Parabolic equations involving Bessel operators and singular integrals