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

Authors
Arash Ghorbanalizadeh
Monire Mikaeili nia
IASBS
Abstract
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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