scholarly journals Control of pseudodifferential operators by maximal functions via weighted inequalities

2018 ◽  
Vol 371 (5) ◽  
pp. 3117-3143 ◽  
Author(s):  
David Beltran
Keyword(s):  
Pseudodifferential Operators ◽  
Maximal Functions ◽  
Weighted Inequalities

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 Inequalities for One-Sided Maximal Functions

1990 ◽  
Vol 319 (2) ◽  
pp. 517 ◽  
Author(s):  
F. J. Martin-Reyes ◽  
P. Ortega Salvador ◽  
A. De La Torre
Keyword(s):  
Maximal Functions ◽  
Weighted Inequalities

scholarly journals MIXED NORM INEQUALITIES FOR SOME DIRECTIONAL MAXIMAL OPERATORS

2012 ◽  
Vol 86 (3) ◽  
pp. 448-455
Author(s):  
DAH-CHIN LUOR
Keyword(s):  
Harmonic Analysis ◽  
Maximal Functions ◽  
Maximal Operators ◽  
Mixed Norm ◽  
Weighted Inequalities ◽  
Norm Inequalities ◽  
One Dimensional

AbstractMixed norm inequalities for directional operators are closely related to the boundedness problems of several important operators in harmonic analysis. In this paper we prove weighted inequalities for some one-dimensional one-sided maximal functions. Then by applying these results, we establish mixed norm inequalities for directional maximal operators which are defined from these one-dimensional maximal functions. We also estimate the constants in these inequalities.

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 Weighted inequalities for anisotropic maximal functions

1985 ◽  
Vol 110 (4) ◽  
pp. 384-393
Author(s):  
Vachtang Michailovič Kokilashvili ◽  
Jiří Rákosník
Keyword(s):  
Maximal Functions ◽  
Weighted Inequalities
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