Commutators of Calderón-Zygmund operators related to admissible functions on spaces of homogeneous type and applications to Schrödinger operators

Liu, Yu; Huang, Jingyun; Dong, Jianfeng

doi:10.1007/s11425-012-4551-3

Cited by 20 publications

(10 citation statements)

References 36 publications

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“…In fact, the characterizations of spaces of functions or distributions, including the atomic and molecular characterizations, have many important applications in harmonic analysis. In recent years, it has been proved that many results in the classical theory of Hardy spaces and singular integrals can transplant to the function spaces associated with operators, such as [30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Herz-Type Hardy Spaces Associated with Operators

Chai

Yan

Zhao

2018

Journal of Function Spaces

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Suppose is a nonnegative, self-adjoint differential operator. In this paper, we introduce the Herz-type Hardy spaces associated with operator . Then, similar to the atomic and molecular decompositions of classical Herz-type Hardy spaces and the Hardy space associated with operators, we prove the atomic and molecular decompositions of the Herz-type Hardy spaces associated with operator . As applications, the boundedness of some singular integral operators on Herz-type Hardy spaces associated with operators is obtained.

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Section: Introductionmentioning

confidence: 99%

Herz-Type Hardy Spaces Associated with Operators

Chai

Yan

Zhao

2018

Journal of Function Spaces

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“…In recent years, more scholars pay attention to the boundedness of the commutators [b,T] when T are the singular integral operators associated with the Schrödinger operator (cf. [1,[6][7][8][9][10][11]). When the potential V satisfies the weaker condition, the operator T may not be a Calderón-Zygmund operator.…”

Section: Introductionmentioning

confidence: 99%

Commutators of Singular Integral Operators Related to Magnetic Schrödinger Operators

Liu¹

2018

ATA

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“…Note that if θ = 0, then θ ν (H n , ρ) is the classical Campanato space; if ν = 0, then θ ν (H n , ρ) is the space BMO θ (H n , ρ) introduced in [3]; see also [25].…”

Section: Introductionmentioning

confidence: 99%

Morrey-type estimates for commutator of fractional integral associated with Schrödinger operators on the Heisenberg group

2018

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Let L =-H n + V be a Schrödinger operator on the Heisenberg group H n , where the nonnegative potential V belongs to the reverse Hölder class RH q 1 for some q 1 ≥ Q/2, and Q is the homogeneous dimension of H n. Let b belong to a new Campanato space θ ν (ρ), and let I L β be the fractional integral operator associated with L. In this paper, we study the boundedness of the commutators [b, I L β ] with b ∈ θ ν (ρ) on central generalized Morrey spaces LM α,V p,ϕ (H n), generalized Morrey spaces M α,V p,ϕ (H n), and vanishing generalized Morrey spaces VM α,V p,ϕ (H n) associated with Schrödinger operator, respectively. When b belongs to θ ν (ρ) with θ > 0, 0 < ν < 1 and (ϕ 1 , ϕ 2) satisfies some conditions, we show that the commutator operator [b, I L β ] is bounded from LM α,V p,ϕ 1 (H n) to LM α,V q,ϕ 2 (H n), from M α,V p,ϕ 1 (H n) to M α,V q,ϕ 2 (H n), and from VM α,V p,ϕ 1 (H n) to VM α,V q,ϕ 2 (H n), 1/p-1/q = (β + ν)/Q.

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Commutators of Calderón-Zygmund operators related to admissible functions on spaces of homogeneous type and applications to Schrödinger operators

Cited by 20 publications

References 36 publications

Herz-Type Hardy Spaces Associated with Operators

Herz-Type Hardy Spaces Associated with Operators

Commutators of Singular Integral Operators Related to Magnetic Schrödinger Operators

Morrey-type estimates for commutator of fractional integral associated with Schrödinger operators on the Heisenberg group

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