Fredholm multiplication operators between Holder spaces

Abstract. Let U be an open bounded subset of R^d. We aim to investigate the multiplication operator on Hölder space C^{۱,۱}(U), specifically focusing on Fredholm operators. Our goal is to provide an interpretation of these operators in these spaces and to discuss and prove their properties. In the case where U is a subset of R, we present and prove results regarding these operators. Furthermore, we establish a necessary condition for the Fredholm property of these operators.

کلیدواژه ها:

Banach space ، Hölder space ، Differentiable functions ، multiplication operator ، Fredholm operator