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 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{&#x0393;}) and the generalized Morrey space {M}_{p,\varphi }(\text{&#x0393;}) defined on Carleson curves \text{&#x0393;} , 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{&#x0393;}) and the strong and weak Adams-type boundedness on {M}_{p,\varphi }(\text{&#x0393;}) .

scholarly journals Sublinear operators with rough kernel on generalized Morrey spaces

1998 ◽  
Vol 27 (1) ◽  
pp. 219-232 ◽  
Author(s):  
Shanzhen LU ◽  
Dachun YANG ◽  
Zusheng ZHOU
Keyword(s):  
Morrey Spaces ◽  
Rough Kernel ◽  
Generalized Morrey Spaces ◽  
Sublinear Operators

Weighted boundedness for Toeplitz type operator associated to general integral operators

2014 ◽  
Vol 07 (02) ◽  
pp. 1450026
Author(s):  
Lanzhe Liu
Keyword(s):  
Maximal Function ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Type Operator ◽  
Sharp Maximal Function ◽  
Riesz Operator ◽  
Marcinkiewicz Operator ◽  
Bmo Functions ◽  
General Integral ◽  
Toeplitz Type Operator

In this paper, we establish the weighted sharp maximal function estimates for the Toeplitz type operators associated to some integral operators and the weighted Lipschitz and BMO functions. As an application, we obtain the boundedness of the Toeplitz type operators on weighted Lebesgue and Morrey spaces. The operator includes Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.

Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces

2011 ◽  
Vol 71 (3) ◽  
pp. 327-355 ◽  
Author(s):  
Vagif S. Guliyev ◽  
Seymur S. Aliyev ◽  
Turhan Karaman ◽  
Parviz S. Shukurov
Keyword(s):  
Morrey Spaces ◽  
Generalized Morrey Spaces ◽  
Sublinear Operators

scholarly journals Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

2016 ◽  
Vol 14 (1) ◽  
pp. 1023-1038
Author(s):  
Ali Akbulut ◽  
Amil Hasanov
Keyword(s):  
Fractional Integral ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Higher Order ◽  
Integral Inequalities ◽  
Rough Kernels ◽  
Weighted Morrey Spaces ◽  
Type Integral

AbstractIn this paper, we study the boundedness of fractional multilinear integral operators with rough kernels $T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces Mp,ϕ (w). We find the sufficient conditions on the pair (ϕ1, ϕ2) with w ∈ Ap,q which ensures the boundedness of the operators $T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ from ${M_{p,{\varphi _1}}}\left( {{w^p}} \right)\,{\rm{to}}\,{M_{p,{\varphi _2}}}\left( {{w^q}} \right)$ for 1 < p < q < ∞. In all cases the conditions for the boundedness of the operator $T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ are given in terms of Zygmund-type integral inequalities on (ϕ1, ϕ2) and w, which do not assume any assumption on monotonicity of ϕ1 (x,r), ϕ2(x, r) in r.

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.

Sign in / Sign up

Export Citation Format

Share Document