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Inequalities for Higher Order Riesz-Laguerre Transforms
Department of Physics and Mathematics, Faculty of Education, Sinnar University, Sinnar, Sudan
Department of Mathematics, University of Albutana, Ruffa’a, Sudan
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
- 1 Department of Physics and Mathematics, Faculty of Education, Sinnar University, Sinnar, Sudan
- 2 Department of Mathematics, University of Albutana, Ruffa’a, Sudan
- 3 Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
Advances in Pure Mathematics·Volume 12 (2022)·Pages 332–347·Published 6 April 2022·DOI10.4236/apm.2022.124025
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Abstract
The weak-type (1, 1) boundedness of the higher order Riesz-Laguerre transforms associated with the Laguerre polynomials and the boundedness for the Riesz-Laguerre transforms of order 2 are considered. We discuss a polynomial weight w that makes the Riesz-Laguerre transforms of order greater than or equal to 2 continuous from L 1 ( wd μ α ) into L 1, ∞ ( d μ α ), under specific value α , where μ α is the Laguerre measure.
KeywordsRiesz-Laguerre TransformPolynomial ExpansionWeak-TypeStein Complex Interpolation TheoremCalderon-Zygmund-TypeRiesz-Gauss Transform
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