scholarly journals Weighted norm estimates for gradients of half-space extensions

1995 ◽  
Vol 44 (3) ◽  
pp. 0-0 ◽  
Author(s):  
Richard L. Wheeden ◽  
J. Michael Wilson
Keyword(s):  
Half Space ◽  
Weighted Norm ◽  
Norm Estimates

scholarly journals Bergman norm estimates of Poisson integrals

2001 ◽  
Vol 161 ◽  
pp. 85-125 ◽  
Author(s):  
Boo Rim Choe ◽  
Hyungwoon Koo ◽  
Heungsu Yi
Keyword(s):  
Half Space ◽  
Integrability Condition ◽  
Positive Function ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Norm Estimates ◽  
Harmonic Bergman Space ◽  
Poisson Integrals ◽  
Weighted Integrability

On the half space Rn × R+, it has been known that harmonic Bergman space bp can contain a positive function only if . Thus, for , Poisson integrals can be bp-functions only by means of their boundary cancellation properties. In this paper, we describe what those cancellation properties explicitly are. Also, given such cancellation properties, we obtain weighted norm inequalities for Poisson integrals. As a consequence, under weighted integrability condition given by our weighted norm inequalities, we show that our cancellation properties are equivalent to the bp-containment of Poisson integrals for p under consideration. Our results are sharp in the sense that orders of our weights cannot be improved.

A criterion on oscillation and variation for the commutators of singular integral operators

2015 ◽  
Vol 27 (1) ◽  
Author(s):  
Feng Liu ◽  
Huoxiong Wu
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Weighted Norm ◽  
Norm Estimates ◽  
Variation Operators

AbstractThis paper gives a criterion on the weighted norm estimates of the oscillatory and variation operators for the commutators of Calderón–Zygmund singular integrals in dimension 1. As applications, the weighted

scholarly journals Sharp weighted norm estimates beyond Calderón–Zygmund theory

2016 ◽  
Vol 9 (5) ◽  
pp. 1079-1113 ◽  
Author(s):  
Frédéric Bernicot ◽  
Dorothee Frey ◽  
Stefanie Petermichl
Keyword(s):  
Weighted Norm ◽  
Norm Estimates

Weighted Norm Estimates for the Fourier Transform with a Pair of Weights

1990 ◽  
Vol 318 (1) ◽  
pp. 355 ◽  
Author(s):  
Jan-Olov Stromberg ◽  
Richard L. Wheeden
Keyword(s):  
Fourier Transform ◽  
Weighted Norm ◽  
Norm Estimates ◽  
The Fourier Transform

scholarly journals Some Weighted Norm Estimates for the Composition of the Homotopy and Green’s Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Huacan Li ◽  
Qunfang Li
Keyword(s):  
Convex Domain ◽  
Upper Bound ◽  
Integral Inequality ◽  
Weighted Norm ◽  
Norm Inequalities ◽  
Norm Estimates ◽  
Bounded Convex Domain ◽  
Green’S Operator ◽  
Weighted Integral ◽  
Bounded Convex

We establish theAr(D)-weighted integral inequality for the composition of the HomotopyTand Green’s operatorGon a bounded convex domain and also motivated it to the global domain by the Whitney cover. At the same time, we also obtain some(p,q)-type norm inequalities. Finally, as applications of above results, we obtain the upper bound for theLpnorms ofT(G(u))or(T(G(u)))Bin terms ofLqnorms ofuordu.

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