V. Kokilashvili, A. Meskhi, and S. Samko

On the Correct Formulation of Some Boundary Value Problems for Symmetric Hyperbolic Systems of First Order in a Dihedral Angle

abstract:
The method of approximative inverse operators is applied to the inversion problem for the Riesz potentials $f=I^\al \varphi$, $0< \Re\al< n$, and the characterization of the range $I^\al(L_w^p)$ with densities $\varphi$ in the Lebesgue spaces $L_w^p(\mbrn)$ and a Muckenhoupt weight $w$. The general situation is considered when potentials $f\in L_v^q(\mathbb{R}^n)$, $1<p<\infty$, and $q\ge p$ and Muckenhoupt weights $w$ and $v$ are independent, being related to each other only by integral conditions.

Mathematics Subject Classification: 31B99, 46E35, 46P05, 26A33.

Key words and phrases: Weighted Lebesgue spaces, Riesz potential operator, hypersingular integrals, approximative inverses, Muckenhoupt weights.