scholarly journals Characterizations for the potential operators on Carleson curves in local generalized Morrey spaces

2020 ◽  
Vol 18 (1) ◽  
pp. 1317-1331
Author(s):  
Vagif Guliyev ◽  
Hatice Armutcu ◽  
Tahir Azeroglu
Keyword(s):  
Morrey Space ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Necessary And Sufficient Conditions ◽  
Potential Operator ◽  
Generalized Morrey Space ◽  
Generalized Morrey Spaces ◽  
Potential Operators ◽  
Boundedness Criterion ◽  
Necessary And Sufficient

Abstract In this paper, we give a boundedness criterion for the potential operator { {\mathcal I} }^{\alpha } in the local generalized Morrey space L{M}_{p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) and the generalized Morrey space {M}_{p,\varphi }(\text{Γ}) defined on Carleson curves \text{Γ} , respectively. For the operator { {\mathcal I} }^{\alpha } , we establish necessary and sufficient conditions for the strong and weak Spanne-type boundedness on L{M}_{p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) and the strong and weak Adams-type boundedness on {M}_{p,\varphi }(\text{Γ}) .

scholarly journals Weighted Hardy and Potential Operators in Morrey Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Natasha Samko
Keyword(s):  
Riesz Potential ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Potential Operator ◽  
Potential Operators ◽  
Riesz Potential Operator ◽  
Power Weights ◽  
The One ◽  
Necessary And Sufficient ◽  
Hardy Type Operators

We study the weightedp→q-boundedness of Hardy-type operators in Morrey spacesℒp,λ(ℝn) (orℒp,λ(ℝ+1) in the one-dimensional case) for a class of almost monotonic weights. The obtained results are applied to a similar weightedp→q-boundedness of the Riesz potential operator. The conditions on weights, both for the Hardy and potential operators, are necessary and sufficient in the case of power weights. In the case of more general weights, we provide separately necessary and sufficient conditions in terms of Matuszewska-Orlicz indices of weights.

scholarly journals Necessary and Sufficient Conditions for the Boundedness of Dunkl-Type Fractional Maximal Operator in the Dunkl-Type Morrey Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-10
Author(s):  
Emin Guliyev ◽  
Ahmet Eroglu ◽  
Yagub Mammadov
Keyword(s):  
Maximal Operator ◽  
Morrey Space ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Necessary And Sufficient Conditions ◽  
Dunkl Operator ◽  
Generalized Shift Operator ◽  
Fractional Maximal Operator ◽  
Generalized Shift ◽  
Necessary And Sufficient

We consider the generalized shift operator, associated with the Dunkl operator , . We study the boundedness of the Dunkl-type fractional maximal operator in the Dunkl-type Morrey space , . We obtain necessary and sufficient conditions on the parameters for the boundedness , from the spaces to the spaces , , and from the spaces to the weak spaces , . As an application of this result, we get the boundedness of from the Dunkl-type Besov-Morrey spaces to the spaces , , , , , and .

scholarly journals Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces

2013 ◽  
Vol 21 (2) ◽  
pp. 111-130
Author(s):  
Malik S. Dzhabrailov ◽  
Sevinc Z. Khaligova
Keyword(s):  
Maximal Operator ◽  
Morrey Space ◽  
Riesz Potential ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Potential Operator ◽  
Fractional Maximal Operator ◽  
Riesz Potential Operator ◽  
Necessary And Sufficient ◽  
Limiting Case

Abstract We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/|σ|≤1-1/q≤α/(|σ|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/|σ| ≤ 1/p-1/q≤α ((1-b) |σ|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn).

scholarly journals Potential Operators on Cones of Nonincreasing Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Alexander Meskhi ◽  
Ghulam Murtaza
Keyword(s):  
Mixed Type ◽  
Sufficient Conditions ◽  
Product Type ◽  
Necessary And Sufficient Conditions ◽  
Lebesgue Spaces ◽  
Potential Operators ◽  
Right Hand ◽  
The Right ◽  
Necessary And Sufficient

Necessary and sufficient conditions on weight pairs guaranteeing the two-weight inequalities for the potential operators(Iαf)(x)=∫0∞(f(t)/|x−t|1−α)dtand(ℐα1,α2f)(x,y)=∫0∞∫0∞(f(t,τ)/|x−t|1−α1|y−τ|1−α2)dtdτon the cone of nonincreasing functions are derived. In the case ofℐα1,α2, we assume that the right-hand side weight is of product type. The same problem for other mixed-type double potential operators is also studied. Exponents of the Lebesgue spaces are assumed to be between 1 and ∞.

scholarly journals Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Vagif S. Guliyev ◽  
Seymur S. Aliyev ◽  
Turhan Karaman
Keyword(s):  
Pseudodifferential Operators ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Sublinear Operator ◽  
Generalized Morrey Space ◽  
Riesz Operator ◽  
Generalized Morrey Spaces ◽  
Marcinkiewicz Operator ◽  
Sublinear Operators ◽  
Type Integral

The authors study the boundedness for a large class of sublinear operatorTgenerated by Calderón-Zygmund operator on generalized Morrey spacesMp,φ. As an application of this result, the boundedness of the commutator of sublinear operatorsTaon generalized Morrey spaces is obtained. In the casea∈BMO(ℝn),1<p<∞andTais a sublinear operator, we find the sufficient conditions on the pair (φ1,φ2) which ensures the boundedness of the operatorTafrom one generalized Morrey spaceMp,φ1to anotherMp,φ2. In all cases, the conditions for the boundedness ofTaare given in terms of Zygmund-type integral inequalities on (φ1,φ2), which do not assume any assumption on monotonicity ofφ1,φ2inr. Conditions of these theorems are satisfied by many important operators in analysis, in particular pseudodifferential operators, Littlewood-Paley operator, Marcinkiewicz operator, and Bochner-Riesz operator.

scholarly journals On the boundedness of a generalized fractional integral on generalized Morrey spaces

2002 ◽  
Vol 33 (4) ◽  
pp. 335-340
Author(s):  
Eridani Eridani
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Campanato Space ◽  
Generalized Morrey Space ◽  
Generalized Morrey Spaces ◽  
Generalized Fractional Integral

In this paper we extend Nakai's result on the boundedness of a generalized fractional integral operator from a generalized Morrey space to another generalized Morrey or Campanato space.

scholarly journals Parameter θ -Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Guanghui Lu
Keyword(s):  
Measure Space ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Metric Measure Space ◽  
Marcinkiewicz Integral ◽  
Generalized Morrey Space ◽  
Generalized Morrey Spaces ◽  
Formula Type

Let X , d , μ be a nonhomogeneous metric measure space satisfying the upper doubling and geometrically doubling conditions in the sense of Hytönen. In this setting, the author proves that parameter θ -type Marcinkiewicz integral M θ ρ is bounded on the weighted generalized Morrey space L p , ϕ , τ ω for p ∈ 1 , ∞ . Furthermore, the boudedness of M θ ρ on weak weighted generalized Morrey space W L p , ϕ , τ ω is also obtained.

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