scholarly journals Weak-type and end-point norm estimates for Hardy operators

2020 ◽  
Vol 199 (6) ◽  
pp. 2381-2393
Author(s):  
Santiago Boza ◽  
Javier Soria
Keyword(s):  
Weak Type ◽  
Norm Estimates ◽  
End Point ◽  
Hardy Operators

scholarly journals On weighted weak type inequalities for modified Hardy operators

1998 ◽  
Vol 126 (6) ◽  
pp. 1739-1746 ◽  
Author(s):  
F. J. Martín-Reyes ◽  
P. Ortega
Keyword(s):  
Weak Type ◽  
Hardy Operators

scholarly journals Two-Weight, Weak-Type Norm Inequalities for Fractional Integral Operators and Commutators on Weighted Morrey and Amalgam Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-23
Author(s):  
Hua Wang
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Weak Type ◽  
Extreme Case ◽  
Fractional Integral Operator ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
Norm Estimates ◽  
Symbol Function ◽  
Amalgam Spaces

Let 0<γ<n and Iγ be the fractional integral operator of order γ, Iγfx=∫ℝnx−yγ−nfydy and let b,Iγ be the linear commutator generated by a symbol function b and Iγ, b,Iγfx=bx⋅Iγfx−Iγbfx. This paper is concerned with two-weight, weak-type norm estimates for such operators on the weighted Morrey and amalgam spaces. Based on weak-type norm inequalities on weighted Lebesgue spaces and certain Ap-type conditions on pairs of weights, we can establish the weak-type norm inequalities for fractional integral operator Iγ as well as the corresponding commutator in the framework of weighted Morrey and amalgam spaces. Furthermore, some estimates for the extreme case are also obtained on these weighted spaces.

scholarly journals Weak and strong type estimates for multilinear Calderón–Zygmund operators on differential forms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xuexin Li ◽  
Yuming Xing ◽  
Jinling Niu
Keyword(s):  
Weak Type ◽  
Differential Forms ◽  
Strong Type ◽  
End Point ◽  
Poincaré Type Inequalities

AbstractIn this paper, we define the multilinear Calderón–Zygmund operators on differential forms and prove the end-point weak type boundedness of the operators. Based on nonhomogeneous A-harmonic tensor, the Poincaré-type inequalities for multilinear Calderón–Zygmund operators on differential forms are obtained.

scholarly journals Estimates for Compositions of Maximal Operators with Singular Integrals

2013 ◽  
Vol 56 (4) ◽  
pp. 801-813 ◽  
Author(s):  
Richard Oberlin
Keyword(s):  
Singular Integrals ◽  
Weak Type ◽  
Operator Norm ◽  
Maximal Operators ◽  
Multiplier Operator ◽  
Norm Estimates ◽  
Variation Norm

Abstract.We prove weak-type (1, 1) estimates for compositions of maximal operators with singular integrals. Our main object of interest is the operator Δ*Ψ where Δ* is Bourgain’s maximal multiplier operator and is the sum of several modulated singular integrals; here our method yields a significantly improved bound for the Lq operator norm when 1 < q < 2. We also consider associated variation-norm estimates.

scholarly journals Weighted weak-type inequalities for generalized Hardy operators

2006 ◽  
Vol 2006 ◽  
pp. 1-10
Author(s):  
A. L. Bernardis ◽  
F. J. Martín-Reyes ◽  
P. Ortega Salvador
Keyword(s):  
Weak Type ◽  
Hardy Operators

scholarly journals Two-Weight, Weak-Type Norm Inequalities for a Class of Sublinear Operators on Weighted Morrey and Amalgam Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Hua Wang
Keyword(s):  
Weak Type ◽  
Integral Operators ◽  
Lebesgue Spaces ◽  
Norm Inequalities ◽  
Norm Estimates ◽  
Weighted Lebesgue Spaces ◽  
Sublinear Operators ◽  
Amalgam Spaces

Let Tα0≤α<n be a class of sublinear operators satisfying certain size conditions introduced by Soria and Weiss, and let b,Tα0≤α<n be the commutators generated by BMORn functions and Tα. This paper is concerned with two-weight, weak-type norm estimates for these sublinear operators and their commutators on the weighted Morrey and amalgam spaces. Some boundedness criteria for such operators are given, under the assumptions that weak-type norm inequalities on weighted Lebesgue spaces are satisfied. As applications of our main results, we can obtain the weak-type norm inequalities for several integral operators as well as the corresponding commutators in the framework of weighted Morrey and amalgam spaces.

Hardy operators on weighted amalgams

2010 ◽  
Vol 140 (1) ◽  
pp. 175-188 ◽  
Author(s):  
Pedro Ortega Salvador ◽  
Consuelo Ramírez Torreblanca
Keyword(s):  
Weak Type ◽  
Hardy Operator ◽  
Hardy Operators

We characterize the boundedness of the Hardy operator between weighted amalgams, a problem studied, but not completely solved, by C. Carton-Lebrun, H. P. Heinig and S. C. Hofmann. We also characterize the weighted weak-type inequalities for modified Hardy operators on amalgams.

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