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 + 4ν pn in L p,ν R + n .
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