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 Lp? 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 Lp??regularity of sectorial operators is established. This paper also investigates the trace of the maximal regularity space E01,p?I, together with the imbedding property of E01,p?I into the range-varying function space C?I,X1?1/p?,p?. Finally, a type of semilinear evolution equations with domain-varying nonlinearities is taken into account.