A mapping property of the heat volume potential (Q6564819)

The paper under review deals with mapping properties of the volume potential for the heat equation in anisotropic Hölder spaces. More precisely, the author considers the heat volume potential \(P[f]\) associated to a function \(f\) in the parabolic cylinder \(\Omega_T=\overline{]-\infty,T[}\times \Omega\) and prove that \(P[\cdot]\) is a bounded linear operator from \(C^{\frac{-1+\alpha}{2};\beta}(\overline{\Omega_T})\) to \(C^{\frac{1+\alpha}{2};1+\alpha}(\overline{\Omega_T})\). Then the author applies the obtained results to Dirichlet and Neumann problems for the equation\N\[\N\partial_t u-\Delta u=\partial_t f\, .\N\]