scholarly journals Weighted boundedness of multilinear integral operators for the endpoint cases

2022 ◽  
Vol 7 (4) ◽  
pp. 5690-5711
Author(s):  
Ancheng Chang ◽  
Keyword(s):  
Integral Operators ◽  
Multilinear Operators ◽  
Riesz Operator ◽  
Marcinkiewicz Operators

<abstract><p>We prove the weighted boundedness for the multilinear operators associated to some integral operators for the endpoint cases. The operators include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.</p></abstract>

Boundedness for Multilinear Singular Integral Operators on Some Hardy and Herz Type Spaces

2005 ◽  
Vol 12 (2) ◽  
pp. 309-320
Author(s):  
Lanzhe Liu
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lipschitz Functions ◽  
Multilinear Operators ◽  
Multilinear Singular Integral ◽  
Type Spaces

Abstract In this paper, we prove the boundedness for some multilinear operators generated by singular integral operators and Lipschitz functions on some Hardy and Herz type spaces.

Endpoint estimates for multilinear operators of some sublinear operators on Herz and Herz type Hardy spaces

2005 ◽  
Vol 42 (2) ◽  
pp. 131-151
Author(s):  
L. Liu
Keyword(s):  
Hardy Spaces ◽  
Integral Operators ◽  
Multilinear Operators ◽  
Marcinkiewicz Operator ◽  
Sublinear Operators

In this paper the endpoint estimates for some multilinear operators related to certain sublinear integral operators on Herz and Herz type Hardy spaces are obtained. The operators include Littlewood-Paley operator and Marcinkiewicz operator.

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 Estimates of multilinear singular integral operators and mean oscillation

2014 ◽  
Vol 95 (109) ◽  
pp. 201-214
Author(s):  
Lanzhe Liu
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Orlicz Spaces ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Multilinear Operators ◽  
Lebesgue Spaces ◽  
Marcinkiewicz Operator ◽  
Mean Oscillation

We prove the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces. The operators include Calder?n-Zygmund singular integral operator, Littlewood-Paley operator and Marcinkiewicz operator.

scholarly journals On the Theory of Multilinear Singular Operators with Rough Kernels on the Weighted Morrey Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Sha He ◽  
Xiangxing Tao
Keyword(s):  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Multilinear Operators ◽  
Rough Kernels ◽  
Fractional Integral Operators ◽  
Weighted Morrey Spaces ◽  
Maximal Singular Integral

We study some multilinear operators with rough kernels. For the multilinear fractional integral operatorsTΩ,αAand the multilinear fractional maximal integral operatorsMΩ,αA, we obtain their boundedness on weighted Morrey spaces with two weightsLp,κ(u,v)whenDγA∈Λ˙β  (|γ|=m-1)orDγA∈BMO  (|γ|=m-1). For the multilinear singular integral operatorsTΩAand the multilinear maximal singular integral operatorsMΩA, we show they are bounded on weighted Morrey spaces with two weightsLp,κ(u,v)ifDγA∈Λ˙β  (|γ|=m-1)and bounded on weighted Morrey spaces with one weightLp,κ(w)ifDγA∈BMO  (|γ|=m-1)form=1,2.

scholarly journals Boundedness of Toeplitz type operators associated to Riesz potential operator with general kernel on Orlicz space

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Dazhao Chen
Keyword(s):  
Integral Operator ◽  
Riesz Potential ◽  
Orlicz Spaces ◽  
Integral Operators ◽  
Potential Operator ◽  
Lebesgue Spaces ◽  
Riesz Operator ◽  
Marcinkiewicz Operator ◽  
General Integral ◽  
Riesz Potential Operator

AbstractIn this paper, the boundedness properties for some Toeplitz type operators associated to the Riesz potential and general integral operators from Lebesgue spaces to Orlicz spaces are proved. The general integral operators include singular integral operator with general kernel, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

scholarly journals Hardy spaces estimates for multilinear operators with homogeneous kernels

2003 ◽  
Vol 170 ◽  
pp. 117-133 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Fractional Integral ◽  
Integral Operators ◽  
Kernel Functions ◽  
Multilinear Operators ◽  
Product Spaces ◽  
Bounded Operators ◽  
Fractional Integral Operators ◽  
Bmo Function

AbstractIn this paper the authors prove that a class of multilinear operators formed by the singular integral or fractional integral operators with homogeneous kernels are bounded operators from the product spaces Lp1 × Lp2 × · · · × LpK (ℝn) to the Hardy spaces Hq (ℝn) and the weak Hardy space Hq,∞(ℝn), where the kernel functions Ωij satisfy only the Ls-Dini conditions. As an application of this result, we obtain the (Lp, Lq) boundedness for a class of commutator of the fractional integral with homogeneous kernels and BMO function.

scholarly journals Sharp maximal function estimates and boundedness for commutators associated with general integral operator

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 137-151 ◽  
Author(s):  
Lanzhe Liu
Keyword(s):  
Integral Operator ◽  
Maximal Function ◽  
Lipschitz Functions ◽  
Sharp Maximal Function ◽  
Lizorkin Space ◽  
Riesz Operator ◽  
General Integral ◽  
General Integral Operator ◽  
Marcinkiewicz Operators

In this paper, we establish the sharp maximal function estimates for the commutator associated with some integral operator with general kernel and the weighted Lipschitz functions. As an application, we obtain the boundedness of the commutator on weighted Lebesgue, Morrey and Triebel-Lizorkin space. The operator includes Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.

scholarly journals Lp Estimates for Multilinear Operators of Strongly Singular Integral Operators

2006 ◽  
Vol 181 ◽  
pp. 41-62 ◽  
Author(s):  
Junfeng Li ◽  
Shanzhen Lu
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Multilinear Operators ◽  
Lp Estimates ◽  
Bmo Functions

AbstractIn this paper, the authors get the Lp estimates for the commutators generated by strongly singular integral operators and BMO functions and the corresponding multilinear operators by the scale changing method introduced by Carleson and Sjölin.

Iterating Bilinear Hardy Inequalities

2017 ◽  
Vol 60 (4) ◽  
pp. 955-971 ◽  
Author(s):  
Martin Křepela
Keyword(s):  
Linear Operator ◽  
Simple Proof ◽  
Hardy Inequality ◽  
Integral Operators ◽  
Multilinear Operators ◽  
Hardy Inequalities ◽  
Hardy Type ◽  
Image Position ◽  
Iteration Technique

AbstractAn iteration technique for characterizing boundedness of certain types of multilinear operators is presented, reducing the problem to a corresponding linear-operator case. The method gives a simple proof of a characterization of validity of the weighted bilinear Hardy inequalityfor all non-negative f, g on (a, b), for 1 < p1, p2, q < ∞. More equivalent characterizing conditions are presented.The same technique is applied to various further problems, in particular those involving multilinear integral operators of Hardy type.

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