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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Main Authors: Mohammed Ali, Hussain Al-Qassem
Format: Article
Language:English
Published: MDPI AG 2022-10-01
Series:Mathematics
Subjects:
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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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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