Weighted norm inequalities for operators of potential type and fractional maximal functions

1996 ◽  
Vol 5 (6) ◽  
pp. 523-580 ◽  
Author(s):  
Eric T. Sawyer ◽  
Richard L. Wheeden ◽  
Shiying Zhao
Keyword(s):  
Maximal Functions ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Potential Type ◽  
Inequalities For Operators

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 .

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