Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions

Castro, Alejandro J.; Fariña, Juan C.; Rodríguez-Mesa, Lourdes

doi:10.1016/j.jmaa.2015.05.069

Cited by 7 publications

(3 citation statements)

References 46 publications

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“…There has since been numerous investigations into harmonic analysis associated to this operator. See for example [BFBMT,BCFR,BCFR2,BFS,BDT,BHNV,DLWY,V,YY].…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

“…We mention that the inequality was proved in [BCFR2] for p = 2. However, an iteration argument shows that it also holds for general p > 0.…”

Section: Moser Type Inequalitymentioning

confidence: 92%

“…Moser type inequality. As the Moser type inequality, established in [BCFR2,p. 454], we mean the following: For any…”

Section: Heat Kernel and Poisson Kernel Estimatesmentioning

confidence: 99%

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Product Hardy, BMO spaces and iterated commutators associated with Bessel Schrodinger operators

Duong¹,

Li²,

Wick

et al. 2019

Indiana Univ. Math. J.

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In this paper we establish the product Hardy spaces associated with the Bessel Schrödinger operator introduced by Muckenhoupt and Stein, and provide equivalent characterizations in terms of the Bessel Riesz transforms, non-tangential and radial maximal functions, and Littlewood-Paley theory, which are consistent with the classical product Hardy space theory developed by Chang and Fefferman. Moreover, in this specific setting, we also provide another characterization via the Telyakovskií transform, which further implies that the product Hardy space associated with this Bessel Schrödinger operator is isomorphic to the subspace of suitable "odd functions" in the standard Chang-Fefferman product Hardy space. Based on the characterizations of these product Hardy spaces, we study the boundedness of the iterated commutator of the Bessel Riesz transforms and functions in the product BMO space associated with Bessel Schrödinger operator. We show that this iterated commutator is bounded above, but does not have a lower bound. √ S λ or T t := e −tS λ .We now define the product Hardy space via the Littlewood-Paley area functions as follows.We now define another version of the Littlewood-Paley area function. Let ∇ t 1 , y 1 := (∂ t 1 , ∂ y 1 ), ∇ t 2 , y 2 := (∂ t 2 , ∂ y 2 ). Then the Littlewood-Paley area function∇ t 1 , y 1 e −t 1 √ S λ ∇ t 2 , y 2 e −t 2 √ S λ (f )(y 1 , y 2 ) 2 dy 1 dy 2 dt 1 dt 2 1 2. (1.4)

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“…There has since been numerous investigations into harmonic analysis associated to this operator. See for example [BFBMT,BCFR,BCFR2,BFS,BDT,BHNV,DLWY,V,YY].…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

“…We mention that the inequality was proved in [BCFR2] for p = 2. However, an iteration argument shows that it also holds for general p > 0.…”

Section: Moser Type Inequalitymentioning

confidence: 92%

See 1 more Smart Citation

Product Hardy, BMO spaces and iterated commutators associated with Bessel Schrodinger operators

Duong¹,

Li²,

Wick

et al. 2019

Indiana Univ. Math. J.

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Bounded Bessel-type operators on $$\textrm{BMO}^{2}_{\alpha }({\mathbb {R}}_{+})$$

2023

J Geom Anal

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Boundedness of Operators on Weighted Morrey–Campanato Spaces in the Bessel Setting

Hu,

Betancor,

Liu

et al. 2024

J Geom Anal

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Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions

Abstract: We consider the Weinstein type equation, with λ > 1. In this paper we characterize the solutions of L λ u = 0 on (0, ∞) × (0, ∞) representable by Bessel-Poisson integrals of BMO-functions as the ones satisfying certain Carleson properties.

Cited by 7 publications

References 46 publications

Product Hardy, BMO spaces and iterated commutators associated with Bessel Schrodinger operators

Product Hardy, BMO spaces and iterated commutators associated with Bessel Schrodinger operators

Bounded Bessel-type operators on $$\textrm{BMO}^{2}_{\alpha }({\mathbb {R}}_{+})$$

Boundedness of Operators on Weighted Morrey–Campanato Spaces in the Bessel Setting

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