Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains
We prove <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mi>p</mi></msup></semantics></math></inline-formula> estimates of a class of generalized...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/6/596 |
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| author | Mohammed Ali Hussain Al-Qassem |
| author_facet | Mohammed Ali Hussain Al-Qassem |
| author_sort | Mohammed Ali |
| collection | DOAJ |
| description | We prove <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mi>p</mi></msup></semantics></math></inline-formula> estimates of a class of generalized Marcinkiewicz integral operators with mixed homogeneity on product domains. By using these estimates along with an extrapolation argument, we obtain the boundedness of our operators under very weak conditions on the kernel functions. Our results in this paper improve and extend several known results on both generalized Marcinkiewicz integrals and parabolic Marcinkiewicz integrals on product domains. |
| first_indexed | 2024-03-11T02:46:57Z |
| format | Article |
| id | doaj.art-9a330d98ee6a424380513740fea6201a |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T02:46:57Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-9a330d98ee6a424380513740fea6201a2023-11-18T09:17:15ZengMDPI AGAxioms2075-16802023-06-0112659610.3390/axioms12060596Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product DomainsMohammed Ali0Hussain Al-Qassem1Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, JordanMathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, Doha 2713, QatarWe prove <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mi>p</mi></msup></semantics></math></inline-formula> estimates of a class of generalized Marcinkiewicz integral operators with mixed homogeneity on product domains. By using these estimates along with an extrapolation argument, we obtain the boundedness of our operators under very weak conditions on the kernel functions. Our results in this paper improve and extend several known results on both generalized Marcinkiewicz integrals and parabolic Marcinkiewicz integrals on product domains.https://www.mdpi.com/2075-1680/12/6/596Triebel–Lizorkin spacerough kernelparabolic Marcinkiewicz integralproduct domainsextrapolation |
| spellingShingle | Mohammed Ali Hussain Al-Qassem Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains Axioms Triebel–Lizorkin space rough kernel parabolic Marcinkiewicz integral product domains extrapolation |
| title | Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains |
| title_full | Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains |
| title_fullStr | Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains |
| title_full_unstemmed | Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains |
| title_short | Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains |
| title_sort | estimates for generalized parabolic marcinkiewicz integrals with rough kernels on product domains |
| topic | Triebel–Lizorkin space rough kernel parabolic Marcinkiewicz integral product domains extrapolation |
| url | https://www.mdpi.com/2075-1680/12/6/596 |
| work_keys_str_mv | AT mohammedali estimatesforgeneralizedparabolicmarcinkiewiczintegralswithroughkernelsonproductdomains AT hussainalqassem estimatesforgeneralizedparabolicmarcinkiewiczintegralswithroughkernelsonproductdomains |