arXiv subjects

Mouna Chegaar

Publications and source records attributed to Mouna Chegaar.

3 recordsLinked to original sources

arXiv2025

Fractional Bessel-Sobolev and Bessel B-potential spaces

After proving the equivalence of the Bessel $K$-functional and the corresponding spherical modulus of smoothness we define fractional Bessel-Sobolev spaces. As an analog of the classical one the imbedding relation of fractional Bessel-Sobolev and Bessel B-potential spaces is pointed out. Applying the defined notions a potential theoretic characterization of removable sets with respect to certain fractional partial differential operator is derived.

math.CA↗

arXiv2025

Removable Sets for Fractional Heat and Fractional Bessel-Heat Equations

We examine the fractional heat diffusion equations $L_{\gamma,a}:=(-\Delta_a)^{\frac{\gamma}{2}}+\partial_t$, where $\Delta_a$ is the Laplace- or the Bessel-Laplace operator. We give conditions for removability which are sufficient and which are necessary, by $L^p$-capacities. Introducing a spherical modulus of smoothness we can treat the Laplace and Bessel-Laplace cases together.

math.CA↗

arXiv2024

Trace inequality with Bessel convolution

Considering potentials defined by Bessel kernel with Bessel convolution a Kerman-Sawyer type characterization of trace inequality is given. As an application an estimate on the least eigenvalue of Schr\"odinger-Bessel operators is derived.

math.CA↗