The volume potential for elliptic differential operators in Schauder spaces

TL;DR

This paper establishes continuity properties of volume potentials associated with elliptic differential operators in Schauder spaces, extending classical results to negative exponents and generalizing known theorems.

Contribution

It provides new continuity results for volume potentials in Schauder spaces of negative exponents, broadening the theoretical understanding of elliptic operators in these function spaces.

Findings

Proves continuity of volume potentials in Schauder spaces of negative exponent.

Generalizes classical Schauder space results to broader settings.

Extends the theory of elliptic operators in functional analysis.

Abstract

The aim of this paper is to prove continuity results for the volume potential corresponding to the fundamental solution of a second order differential operator with constant coefficients in Schauder spaces of negative exponent and to generalize some classical results in Schauder spaces of positive exponents.