Volume 10, Issue 1 (4-2024)                   mmr 2024, 10(1): 1-17 | Back to browse issues page

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Ghorbanalizadeh A, Mikaeili nia M. On the Boundedness of Littlewood-Paley $ g^{*}_{B, lambda}$   operator associated with Bessel differential operator. mmr 2024; 10 (1) :1-17
URL: http://mmr.khu.ac.ir/article-1-3233-en.html
1- IASBS , gurbanalizade@gmail.com
2- IASBS
Abstract:   (520 Views)
The study of classical Littlewood-Paley operators has an intrinsic interest for their essential role in harmonic analysis due to their applications in PDEs and other fields.
One of the Littlewood-Paley operators is g λ *  operator which its p,p  strong boundedness depends on the parameter λ . For example, Fefferman showed strong boundedness of classical g λ *  for 1<p<∞  in L p   when λ>max 1, 2 p .  In this work, We consider the Laplace-Bessel differential operator and correspondingly we define the relevant Littlewood-Paley operator g B,λ *  to investigate both L p,ν - boundedness of g B,λ *  for 2≤P<∞  and λ>1+ 2v n and its unboundedness for 0<λ< 2 P + pn in L p,ν R + n .
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Type of Study: Original Manuscript | Subject: Anal
Received: 2021/09/5 | Revised: 2024/07/10 | Accepted: 2022/06/12 | Published: 2024/01/8 | ePublished: 2024/01/8

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