Some Embedding Theorems on the Nikolskii-Morrey Type Spaces

Akbulut, Ali; Eroğlu, Ahmet; Najafov, Alik M.

doi:10.22606/aan.2016.11003

Cited by 4 publications

(3 citation statements)

References 1 publication

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“…The Nikolskii-Morrey space H l p,λ (R n ) and Nikolskii-Morrey type space H l p,ϕ,β (G) studied in [1,17]. Also note that in this paper, in theorem 2.2 it was proved that the Holder "index" is larger than in [1,12,14] .…”

Section: Introduction and Preliminary Notesmentioning

confidence: 63%

On Embedding Theorems in Grand Grand Nikolskii-Morrey Spaces

Najafov¹,

Gasimova²

2019

Eur. J. Pure Appl. Math.

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Section: Introduction and Preliminary Notesmentioning

confidence: 63%

On Embedding Theorems in Grand Grand Nikolskii-Morrey Spaces

Najafov¹,

Gasimova²

2019

Eur. J. Pure Appl. Math.

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“…Remark 1.9. Note that, in [2] the Nikolskii-Morrey type spaces were introduced and the authors studied some embedding theorems. In the next paper, we shall introduce the generalized weighted Nikolskii-Morrey spaces and will study some embedding theorems.…”

Section: Introduction and Resultsmentioning

confidence: 99%

Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

Akbulut

Hasanov

2016

Open Mathematics

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Abstract:In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels T A 1 ;A 2 ;:::;A k ;˛, which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces M p;' .w/. We find the sufficient conditions on the pair .' 1 ; ' 2 / with w 2 A p;q which ensures the boundedness of the operators T ;˛a re given in terms of Zygmund-type integral inequalities on .' 1 ; ' 2 / and w, which do not assume any assumption on monotonicity of ' 1 .x; r/; ' 2 .x; r/ in r.

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“…for all x ∈ R n and r > 0, where b B = 1 |B| B b(y) dy. A norm for b ∈ BMO θ (ρ), denoted by [b] θ , is given by the infimum of the constants in the inequalities above.…”

Section: Some Technical Lemmas and Propositionsmentioning

confidence: 99%

Commutator of fractional integral with Lipschitz functions associated with Schrödinger operator on local generalized Morrey spaces

Guliyev

Akbulut

2018

Bound Value Probl

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Let L =-+ V be a Schrödinger operator on R n , where n ≥ 3 and the nonnegative potential V belongs to the reverse Hölder class RH q 1 for some q 1 > n/2. Let b belong to a new Campanato space θ ν (ρ) and 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 local generalized Morrey spaces LM α,V,{x 0 } p,ϕ , generalized Morrey spaces M α,V p,ϕ and vanishing generalized Morrey spaces VM α,V p,ϕ 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 ] are bounded from LM α,V,{x 0 } p,ϕ 1 to LM α,V,{x 0 } q,ϕ 2 , from M α,V p,ϕ 1 to M α,V q,ϕ 2 and from VM α,V p,ϕ 1 to VM α,V q,ϕ 2 , 1/p-1/q = (β + ν)/n.

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Some Embedding Theorems on the Nikolskii-Morrey Type Spaces

Cited by 4 publications

References 1 publication

On Embedding Theorems in Grand Grand Nikolskii-Morrey Spaces

On Embedding Theorems in Grand Grand Nikolskii-Morrey Spaces

Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

Commutator of fractional integral with Lipschitz functions associated with Schrödinger operator on local generalized Morrey spaces

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