Weighted Norm Inequalities for Local Fractional Integrals on Gaussian Measure Spaces

2019 ◽  
Vol 53 (4) ◽  
pp. 1377-1401
Author(s):  
Haibo Lin ◽  
Shengchen Mao
Keyword(s):  
Gaussian Measure ◽  
Fractional Integrals ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Measure Spaces

Sharp function estimates for fractional integrals and related operators

1990 ◽  
Vol 49 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Douglas S. Kurtz
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
Sharp Function ◽  
Multiplier Operators ◽  
Kernel Operators

AbstractThis paper considers analogs of results on integral operators studied by Hörmander. Using the sharp function introduced by Fefferman and Stein, we prove weighted norm inequalities on kernel operators which map an Lp space into an Lq space, with q not equal to p. The techniques recover known results about fractional integral operators and apply to multiplier operators which satisfy a generalization of the Hörmander multiplier condition.

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
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