Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces
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...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/3672892 |
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| _version_ | 1832550512079142912 |
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| author | Qinghua Zhang Yueping Zhu Feng Wang |
| author_facet | Qinghua Zhang Yueping Zhu Feng Wang |
| author_sort | Qinghua Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b168b4c17b7e4ef2b63fe126bd215f60 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-b168b4c17b7e4ef2b63fe126bd215f602025-02-03T06:06:31ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/36728923672892Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue SpacesQinghua Zhang0Yueping Zhu1Feng Wang2School of Sciences, Nantong University, Nantong, ChinaSchool of Sciences, Nantong University, Nantong, ChinaSchool of Sciences, Nantong University, Nantong, ChinaThis 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.http://dx.doi.org/10.1155/2020/3672892 |
| spellingShingle | Qinghua Zhang Yueping Zhu Feng Wang Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces Journal of Function Spaces |
| title | Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces |
| title_full | Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces |
| title_fullStr | Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces |
| title_full_unstemmed | Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces |
| title_short | Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces |
| title_sort | boundedness of singular integral operators with operator valued kernels and maximal regularity of sectorial operators in variable lebesgue spaces |
| url | http://dx.doi.org/10.1155/2020/3672892 |
| work_keys_str_mv | AT qinghuazhang boundednessofsingularintegraloperatorswithoperatorvaluedkernelsandmaximalregularityofsectorialoperatorsinvariablelebesguespaces AT yuepingzhu boundednessofsingularintegraloperatorswithoperatorvaluedkernelsandmaximalregularityofsectorialoperatorsinvariablelebesguespaces AT fengwang boundednessofsingularintegraloperatorswithoperatorvaluedkernelsandmaximalregularityofsectorialoperatorsinvariablelebesguespaces |