Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces. (10th March 2020) - Zhang, Qinghua; Zhu, Yueping; Wang, Feng
Abstract : This paper is devoted to the maximal regularity of sectorial operators in Lebesgue spaces L p ⋅ 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 L p ⋅ − regularity of sectorial operators is established. This paper also investigates the trace of the maximal regularity space E 0 1, p ⋅ I, together with the imbedding property of E 0 1, p ⋅ I into the range-varying function space C − I, X 1 − 1 / p ⋅, p ⋅ . Finally, a type of semilinear evolution equations with domain-varying nonlinearities is taken into account.