Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces. (10th March 2020)

• Record Type: Journal Article
• Authors: Zhang, Qinghua; Zhu, Yueping; Wang, Feng
• Other Names: Han Yongsheng S. Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-03-10
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/3672892
• Languages: English
• ISSNs: 2314-8896

Abstract

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.