Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces

摘要

This paper is devoted to the maximal regularity of sectorial operators in Lebesgue spaces with a variable exponent. By extending the boundedness of singular integral operators in variable Lebesgue spaces from scalar type to abstract-valued type, the maximal regularity of sectorial operators is established. This paper also investigates the trace of the maximal regularity space , together with the imbedding property of into the range-varying function space . Finally, a type of semilinear evolution equations with domain-varying nonlinearities is taken into account.