Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales
Some fundamental properties of the Muckenhoupt class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">A</mi><mi>p</mi></msub></sema...
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MDPI AG
2024-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/13/2/98 |
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| author | Ravi P. Agarwal Mohamed Abdalla Darwish Hamdi Ali Elshamy Samir H. Saker |
| author_facet | Ravi P. Agarwal Mohamed Abdalla Darwish Hamdi Ali Elshamy Samir H. Saker |
| author_sort | Ravi P. Agarwal |
| collection | DOAJ |
| description | Some fundamental properties of the Muckenhoupt class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">A</mi><mi>p</mi></msub></semantics></math></inline-formula> of weights and the Gehring class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">G</mi><mi>q</mi></msub></semantics></math></inline-formula> of weights on time scales and some relations between them will be proved in this paper. To prove the main results, we will apply an approach based on proving some properties of integral operators on time scales with powers and certain mathematical relations connecting the norms of Muckenhoupt and Gehring classes. The results as special cases cover the results for functions following David Cruz-Uribe, C. J. Neugebauer, and A. Popoli, and when the time scale equals the positive integers, the results for sequences are essentially new. |
| first_indexed | 2024-03-07T22:42:25Z |
| format | Article |
| id | doaj.art-3a5154fd28594856af653f91c88302a4 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-07T22:42:25Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-3a5154fd28594856af653f91c88302a42024-02-23T15:07:24ZengMDPI AGAxioms2075-16802024-01-011329810.3390/axioms13020098Fundamental Properties of Muckenhoupt and Gehring Weights on Time ScalesRavi P. Agarwal0Mohamed Abdalla Darwish1Hamdi Ali Elshamy2Samir H. Saker3Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USADepartment of Mathematics, Faculty of Science, Damanhour University, Damanhour 22514, EgyptDepartment of Mathematics, Faculty of Science, Damanhour University, Damanhour 22514, EgyptDepartment of Mathematics, Mansoura University, Mansoura 35516, EgyptSome fundamental properties of the Muckenhoupt class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">A</mi><mi>p</mi></msub></semantics></math></inline-formula> of weights and the Gehring class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">G</mi><mi>q</mi></msub></semantics></math></inline-formula> of weights on time scales and some relations between them will be proved in this paper. To prove the main results, we will apply an approach based on proving some properties of integral operators on time scales with powers and certain mathematical relations connecting the norms of Muckenhoupt and Gehring classes. The results as special cases cover the results for functions following David Cruz-Uribe, C. J. Neugebauer, and A. Popoli, and when the time scale equals the positive integers, the results for sequences are essentially new.https://www.mdpi.com/2075-1680/13/2/98Muckenhoupt classesGehring classestime scalesHölder’s inequalityJensen’s inequalitychain rule |
| spellingShingle | Ravi P. Agarwal Mohamed Abdalla Darwish Hamdi Ali Elshamy Samir H. Saker Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales Axioms Muckenhoupt classes Gehring classes time scales Hölder’s inequality Jensen’s inequality chain rule |
| title | Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales |
| title_full | Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales |
| title_fullStr | Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales |
| title_full_unstemmed | Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales |
| title_short | Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales |
| title_sort | fundamental properties of muckenhoupt and gehring weights on time scales |
| topic | Muckenhoupt classes Gehring classes time scales Hölder’s inequality Jensen’s inequality chain rule |
| url | https://www.mdpi.com/2075-1680/13/2/98 |
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