A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces
Integral equations and inequalities have an important place in time scales and harmonic analysis. The norm of integral operators is one of the important study topics in harmonic analysis. Using the norms in different variable exponent spaces, the boundedness or compactness of the integral operators...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/1/7 |
| _version_ | 1797414395213512704 |
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| author | Lütfi Akın |
| author_facet | Lütfi Akın |
| author_sort | Lütfi Akın |
| collection | DOAJ |
| description | Integral equations and inequalities have an important place in time scales and harmonic analysis. The norm of integral operators is one of the important study topics in harmonic analysis. Using the norms in different variable exponent spaces, the boundedness or compactness of the integral operators are examined. However, the norm of integral operators on time scales has been a matter of curiosity to us. In this study, we prove the equivalence of the norm of the restricted centered fractional maximal diamond-<inline-formula><math display="inline"><semantics><mrow><mi>α</mi></mrow></semantics></math></inline-formula> integral operator <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="normal">M</mi><mrow><mi mathvariant="normal">a</mi><mo>,</mo><mi mathvariant="sans-serif">δ</mi></mrow><mi mathvariant="normal">c</mi></msubsup></mrow></semantics></math></inline-formula> to the norm of the centered fractional maximal diamond-<inline-formula><math display="inline"><semantics><mrow><mi>α</mi></mrow></semantics></math></inline-formula> integral operator <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="normal">M</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">c</mi></msubsup></mrow></semantics></math></inline-formula> on time scales with variable exponent Lebesgue spaces. This study will lead to the study of problems such as the boundedness and compactness of integral operators on time scales. |
| first_indexed | 2024-03-09T05:32:27Z |
| format | Article |
| id | doaj.art-9076e1d22af84b549584db4908ff4474 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T05:32:27Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-9076e1d22af84b549584db4908ff44742023-12-03T12:31:23ZengMDPI AGFractal and Fractional2504-31102021-01-0151710.3390/fractalfract5010007A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue SpacesLütfi Akın0Department of Business Administration, Mardin Artuklu University, 47200 Mardin, TurkeyIntegral equations and inequalities have an important place in time scales and harmonic analysis. The norm of integral operators is one of the important study topics in harmonic analysis. Using the norms in different variable exponent spaces, the boundedness or compactness of the integral operators are examined. However, the norm of integral operators on time scales has been a matter of curiosity to us. In this study, we prove the equivalence of the norm of the restricted centered fractional maximal diamond-<inline-formula><math display="inline"><semantics><mrow><mi>α</mi></mrow></semantics></math></inline-formula> integral operator <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="normal">M</mi><mrow><mi mathvariant="normal">a</mi><mo>,</mo><mi mathvariant="sans-serif">δ</mi></mrow><mi mathvariant="normal">c</mi></msubsup></mrow></semantics></math></inline-formula> to the norm of the centered fractional maximal diamond-<inline-formula><math display="inline"><semantics><mrow><mi>α</mi></mrow></semantics></math></inline-formula> integral operator <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="normal">M</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">c</mi></msubsup></mrow></semantics></math></inline-formula> on time scales with variable exponent Lebesgue spaces. This study will lead to the study of problems such as the boundedness and compactness of integral operators on time scales.https://www.mdpi.com/2504-3110/5/1/7time scalesvariable exponentfractional integralmaximal operator |
| spellingShingle | Lütfi Akın A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces Fractal and Fractional time scales variable exponent fractional integral maximal operator |
| title | A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces |
| title_full | A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces |
| title_fullStr | A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces |
| title_full_unstemmed | A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces |
| title_short | A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces |
| title_sort | new approach for the fractional integral operator in time scales with variable exponent lebesgue spaces |
| topic | time scales variable exponent fractional integral maximal operator |
| url | https://www.mdpi.com/2504-3110/5/1/7 |
| work_keys_str_mv | AT lutfiakın anewapproachforthefractionalintegraloperatorintimescaleswithvariableexponentlebesguespaces AT lutfiakın newapproachforthefractionalintegraloperatorintimescaleswithvariableexponentlebesguespaces |