Boundedness of the fractional maximal operator in local Morrey-type spaces

Burenkov, V. I.; Гогатишвили, Амиран; Guliyev, Vagif S.; Mustafayev, Rza

doi:10.1080/17476930903394697

Cited by 97 publications

(44 citation statements)

References 11 publications

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“…In [20][21][22][23]25,33] and [35] there were obtained sufficient conditions on ϕ 1 and ϕ 2 for the boundedness of the maximal operator M and Calderón-Zygmund operator K from M p,ϕ1 to M p,ϕ2 , 1 < p < ∞ and of the fractional maximal operator M α and Riesz potential operator I α from M p,ϕ1 to M q,ϕ2 , 1 < p < q < ∞ (see also [3][4][5][6][7]). In [35,36] the following condition was imposed on ϕ(x, r):…”

Section: Sublinear Operators and Commutators 329mentioning

confidence: 99%

Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces

Guliyev

Aliyev

Karaman

et al. 2011

Integr. Equ. Oper. Theory

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In this paper the authors study the boundedness for a large class of sublinear operators Tα, α ∈ [0, n) generated by Calderón-Zygmund operators (α = 0) and generated by Riesz potential operator (α > 0) on generalized Morrey spaces Mp,ϕ. As an application of the above result, the boundeness of the commutator of sublinear operators T b,α , α ∈ [0, n) on generalized Morrey spaces is also obtained. In the case b ∈ BM O and T b,α is a sublinear operator, we find the sufficient conditions on the pair (ϕ1, ϕ2) which ensures the boundedness of the operators T b,α , α ∈ [0, n) from one generalized Morrey space Mp,ϕ 1 to another Mq,ϕ 2 with 1/p − 1/q = α/n. In all the cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on (ϕ1, ϕ2), which do not assume any assumption on monotonicity of ϕ1, ϕ2 in r. Conditions of these theorems are satisfied by many important operators in analysis, in particular, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.Mathematics Subject Classification (2010). Primary 42B20, 42B25, 42B35.

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Section: Sublinear Operators and Commutators 329mentioning

confidence: 99%

Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces

Guliyev

Aliyev

Karaman

et al. 2011

Integr. Equ. Oper. Theory

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“…In [12], [13], [14], [16], [20], [28] and [31], sufficient conditions on ϕ 1 and ϕ 2 for the boundedness of the maximal operator M and a Calderón-Zygmund operator K from the generalized Morrey spaces M p,ϕ1 to M p,ϕ2 for 1 < p < ∞ and from M 1,ϕ1 to W M 1,ϕ2 were obtained (see also [34], [2], [1]). In [9], the following condition was imposed on ϕ(x, r):…”

Section: B(x R)| the Lebesgue Measure Of B(x R)mentioning

confidence: 99%

Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

et al. 2014

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“…These inequalities play an important role in the theory of Morrey-type spaces and other topics (see [6], [7] and [9]). It is worth to mention that using characterizations of weighted Hardy inequalities we can show that the characterization of the boundedness of bilinear Hardy inequalities, namely of the inequality…”

Section: Hg(t)mentioning

confidence: 99%

On weighted iterated Hardy-type inequalities

Гогатишвили

Mustafayev

2017

Positivity

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Abstract. In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator T with the Hardy and Copson operators in weighted Lebesgue spaces are proved. New equivalence theorems are obtained for the operator T to be bounded in weighted Lebesgue spaces restricted to the cones of monotone functions, which allow to change the cone of non-decreasing functions to the cone of non-increasing functions and vice versa not changing the operator T . New characterizations of the weighted Hardy-type inequalities on the cones of monotone functions are given. The validity of so-called weighted iterated Hardy-type inequalities are characterized.

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Boundedness of the fractional maximal operator in local Morrey-type spaces

Cited by 97 publications

References 11 publications

Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces

Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces

Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

On weighted iterated Hardy-type inequalities

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