Separable convolution-elliptic operators with parameters

Abstract

The maximal regularity properties of parameter dependent abstract convolutionelliptic equations are investigated. Here find sufficient conditions that guarantee the uniform separability of these problems in L-p spaces. It is established that the corresponding convolution-elliptic operator is sectorial and is also a generator of an analytic semigroup. Finally, these results applied to obtain the uniform maximal regularity for the Cauchy problem for abstract parabolic equation in mixed Lp norms, boundary value problems for anisotropic integro-differential equations and infinite systems of elliptic integro-differential equations with parameters.