scholarly journals A trace problem for associate Morrey potentials

2018 ◽  
Vol 7 (3) ◽  
pp. 407-424 ◽  
Author(s):  
Jie Xiao
Keyword(s):  
Radon Measure ◽  
Morrey Spaces ◽  
Riesz Operator

AbstractAs a solution to the restriction question for associate Morrey potentials (Question 1.1), this paper characterizes a Radon measure μ on {\mathbb{R}^{n}} such that the Riesz operator {I_{\alpha}} maps the associate Morrey spaces {H^{p,\kappa}_{1}\subset H^{p,\kappa}} to the μ-induced Morrey spaces {L^{q,\lambda}_{\mu}\subset L^{q,\lambda}_{\mu,\infty}} continuously. The discovered restriction/trace principle (Theorem 1.2) is brand-new, and its demonstration is non-trivial.

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.

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.

Aggregation equations with gradient potential as Radon measure and initial data in Besov‐Morrey spaces

2020 ◽  
Vol 43 (9) ◽  
pp. 6103-6116
Author(s):  
Marta L. Suleiman ◽  
Juliana C. Precioso ◽  
Andréa C. Prokopczyk
Keyword(s):  
Initial Data ◽  
Radon Measure ◽  
Morrey Spaces

Complex interpolation of the predual of Morrey spaces over measure spaces

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Victor I. Burenkov ◽  
Denny I. Hakim ◽  
Eiichi Nakai ◽  
Yoshihiro Sawano ◽  
Takuya Sobukawa ◽  
...  
Keyword(s):  
Radon Measure ◽  
Duality Theorem ◽  
Interpolation Method ◽  
Morrey Spaces ◽  
Complex Interpolation ◽  
Block Spaces ◽  
Measure Spaces ◽  
Calderón Product

Abstract We prove that block spaces defined on {\mathbb{R}^{n}} with an arbitrary Radon measure, which are known to be the preduals of Morrey spaces, are closed under the first and the second complex interpolation method. The proof of our main theorem uses the duality theorem in the complex interpolation method, the complex interpolation of certain closed subspaces of Morrey spaces, a characterization of the preduals of block spaces, and some formulas related to the Calderón product.

Compact Commutators on Morrey Spaces with Non-Doubling Measures

2008 ◽  
Vol 15 (2) ◽  
pp. 353-376
Author(s):  
Yoshihiro Sawano ◽  
Satoru Shirai
Keyword(s):  
Growth Condition ◽  
Singular Integral ◽  
Radon Measure ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Smooth Functions ◽  
Fractional Integral Operators ◽  
Bmo Functions ◽  
Doubling Measures

Abstract We study multi-commutators on the Morrey spaces generated by BMO functions and singular integral operators or by BMO functions and fractional integral operators. We place ourselves in the setting of coming with a Radon measure μ which satisfies a certain growth condition. The Morrey-boundedness of commutators is established by M. Yan and D. Yang. However, the corresponding assertion of Morrey-compactness is still missing. The aim of this paper is to prove that the multi-commutators are compact if one of the BMO functions can be approximated with compactly supported smooth functions.

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

scholarly journals Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang
Keyword(s):  
Hilbert Transform ◽  
Besov Spaces ◽  
Singular Integrals ◽  
Riesz Transform ◽  
Morrey Spaces ◽  
Riesz Transforms ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Variation Operators

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.

scholarly journals Some estimates for the commutators of multilinear maximal function on Morrey-type space

2021 ◽  
Vol 19 (1) ◽  
pp. 515-530
Author(s):  
Xiao Yu ◽  
Pu Zhang ◽  
Hongliang Li
Keyword(s):  
Maximal Function ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Generalized Morrey Spaces ◽  
Type Space ◽  
Bmo Function ◽  
Mean Oscillation ◽  
Multilinear Maximal Function ◽  
Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

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