A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution
In this article, certain sharp <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 for...
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MDPI AG
2022-10-01
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Online Access: | https://www.mdpi.com/2227-7390/10/20/3727 |
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author | Mohammed Ali Hussain Al-Qassem |
author_facet | Mohammed Ali Hussain Al-Qassem |
author_sort | Mohammed Ali |
collection | DOAJ |
description | In this article, certain sharp <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 for a specific class of generalized Marcinkiewicz operators with mixed homogeneity associated to surfaces of revolution are established. By virtue of Yano’s extrapolation argument, beside these estimates, the <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> boundedness of the aforementioned operators under weaker assumptions on the kernels is confirmed. The obtained results in this article are fundamental extensions and improvements of numerous previously known results on parabolic generalized Marcinkiewicz integrals. |
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issn | 2227-7390 |
language | English |
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spelling | doaj.art-8203f75cd0a3462bb261eedd6e1a4b142023-11-24T01:06:18ZengMDPI AGMathematics2227-73902022-10-011020372710.3390/math10203727A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of RevolutionMohammed 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, QatarIn this article, certain sharp <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 for a specific class of generalized Marcinkiewicz operators with mixed homogeneity associated to surfaces of revolution are established. By virtue of Yano’s extrapolation argument, beside these estimates, the <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> boundedness of the aforementioned operators under weaker assumptions on the kernels is confirmed. The obtained results in this article are fundamental extensions and improvements of numerous previously known results on parabolic generalized Marcinkiewicz integrals.https://www.mdpi.com/2227-7390/10/20/3727extrapolationTriebel–Lizorkin spacegeneralized Marcinkiewiczrough kernels |
spellingShingle | Mohammed Ali Hussain Al-Qassem A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution Mathematics extrapolation Triebel–Lizorkin space generalized Marcinkiewicz rough kernels |
title | A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution |
title_full | A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution |
title_fullStr | A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution |
title_full_unstemmed | A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution |
title_short | A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution |
title_sort | note on a class of generalized parabolic marcinkiewicz integrals along surfaces of revolution |
topic | extrapolation Triebel–Lizorkin space generalized Marcinkiewicz rough kernels |
url | https://www.mdpi.com/2227-7390/10/20/3727 |
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