On the Boundedness of Littlewood-Paley  $ g^{*}_{B, lambda}$   operator associated with Bessel differential operator

Ghorbanalizadeh, Arash; Mikaeili nia, Monire

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

On the Boundedness of Littlewood-Paley $ g^{*}_{B, lambda}$ operator associated with Bessel differential operator

Arash Ghorbanalizadeh

¹, Monire Mikaeili nia²

1- IASBS , gurbanalizade@gmail.com
2- IASBS

Abstract: (458 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 .

Keywords: Littlewood-Paley operators $g^{*}_{lambda}$, strong boundedness, Littlewood-Paley operators $g^{*}_{B, lambda}$ associated with Bessel differential operator, unboundedness of $g^{*}_{B, lambda}$

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