Analysis Mathematica
Volume/Issue:
Volume 38: Issue 3
Максимальная функция на дуальной гипергруппе Лагерра
Authors:
Assal Miloud College of Science, Department of Mathematics, King Khalid University, Abha, 9004 KSA

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Rahmouni Atef Faculty of Sciences, Laboratoire Analyse mathématiques et Applications, Tunis El Manar University, Tunis, 2092 Tunisia

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Taieb Ahmed Faculty of Sciences, Laboratoire Analyse mathématiques et Applications, Tunis El Manar University, Tunis, 2092 Tunisia

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Pages:
161–171
Online Publication Date:
13 Aug 2012
Publication Date:
01 Sep 2012
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10476-012-0301-6
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Abstract  

In this paper, we are interested in the Laguerre hypergroup
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{K} = [0,\infty ) \times \mathbb{R}$$ \end{document}
which is the fundamental manifold of the radial function space for the Heisenberg group. So, we consider the generalized shift operator generated by the dual of the Laguerre hypergroup
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\bigcup\limits_{j \in \mathbb{N}} {\left\{ {(\lambda ,\mu ) \in \mathbb{R}^2 :\mu = \left| \lambda \right|(2j + \alpha + 1),\lambda \ne 0} \right\} \cup \left\{ {(0,\mu ) \in \mathbb{R}^2 :\mu \geqslant 0} \right\}} ,$$ \end{document}
by means of which the maximal function is investigated. For 1 < p ≤ ∞, the Lp()-boundedness and weak L1()-boundedness result for the maximal function is obtained.
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Cover Analysis Mathematica
Analysis Mathematica
Print ISSN:
0133-3852
Online ISSN:
1588-273X

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Analysis Mathematica
Language English
Size B5
Year of
Foundation		 1975
Volumes
per Year		 1
Issues
per Year		 4
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0133-3852 (Print)
ISSN 1588-273X (Online)

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