scholarly journals New Weighted Norm Inequalities for Pseudodifferential Operators and Their Commutators

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
The Anh Bui
Keyword(s):  
Function Space ◽  
Pseudodifferential Operators ◽  
Bmo Space ◽  
Weighted Norm ◽  
Weighted Inequalities ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Bmo Function ◽  
New Class ◽  
Muckenhoupt Class

This paper is dedicated to study weighted inequalities for pseudodifferential operators with amplitudes and their commutators by using the new class of weights and the new BMO function space BMO∞ which are larger than the Muckenhoupt class of weights and classical BMO space BMO, respectively. The obtained results therefore improve substantially some well-known results.

Weighted Lp Boundedness of Pseudodifferential Operators and Applications

2012 ◽  
Vol 55 (3) ◽  
pp. 555-570 ◽  
Author(s):  
Nicholas Michalowski ◽  
David J. Rule ◽  
Wolfgang Staubach
Keyword(s):  
Pseudodifferential Operator ◽  
Wide Class ◽  
Pseudodifferential Operators ◽  
Maximal Functions ◽  
Bounded Mean Oscillation ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Sharp Function ◽  
Mean Oscillation

AbstractIn this paper we prove weighted norm inequalities with weights in the Ap classes, for pseudodifferential operators with symbols in the class that fall outside the scope of Calderón– Zygmund theory. This is accomplished by controlling the sharp function of the pseudodifferential operator by Hardy–Littlewood type maximal functions. Our weighted norm inequalities also yield Lp boundedness of commutators of functions of bounded mean oscillation with a wide class of operators in .

scholarly journals Multiple-weighted norm inequalities for maximal multi-linear singular integrals with non-smooth kernels

2011 ◽  
Vol 141 (4) ◽  
pp. 755-775 ◽  
Author(s):  
Loukas Grafakos ◽  
Liguang Liu ◽  
Dachun Yang
Keyword(s):  
Singular Integrals ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Weighted Estimates ◽  
New Class ◽  
Littlewood Maximal Function ◽  
Smooth Kernels ◽  
Multiple Weights

We obtain weighted norm inequalities for maximal truncated operators of multi-linear singular integrals with non-smooth kernels in the sense of Duong et al. This class of operators extends the class of multi-linear Calderón-Zygmund operators introduced by Coifman and Meyer and includes the higher-order commutators of Calderón. The weighted norm inequalities obtained in this work are with respect to the new class of multiple weights of Lerner et al. The key ingredient in the proof is the introduction of a new multi-sublinear maximal operator that plays the role of the Hardy-Littlewood maximal function in a version of Cotlar's inequality. As applications of these results, new weighted estimates for the mth order Calderón commutators and their maximal counterparts are deduced.

scholarly journals Weighted norm inequalities for a general maximal operator

1988 ◽  
Vol 26 (1-2) ◽  
pp. 327-340 ◽  
Author(s):  
Francisco J. Ruiz ◽  
Jose L. Torrea
Keyword(s):  
Maximal Operator ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities

Weighted Norm Inequalities for Fractional Integral Operators With Rough Kernel

1998 ◽  
Vol 50 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Rough Kernel ◽  
Degree Zero ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
Image Position

AbstractGiven function Ω on ℝn , we define the fractional maximal operator and the fractional integral operator by and respectively, where 0 < α < n. In this paper we study the weighted norm inequalities of MΩα and TΩα for appropriate α, s and A(p, q) weights in the case that Ω∈ Ls(Sn-1)(s> 1), homogeneous of degree zero.

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