scholarly journals Some weak-type estimates for singular integral operators on $CMO$ spaces

2010 ◽  
Vol 39 (1) ◽  
pp. 115-126 ◽  
Author(s):  
Yasuo KOMORI-FURUYA ◽  
Katsuo MATSUOKA
Keyword(s):  
Singular Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Weak Type Estimates

scholarly journals Commutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type

2008 ◽  
Vol 2008 ◽  
pp. 1-21 ◽  
Author(s):  
Guoen Hu ◽  
Haibo Lin ◽  
Dachun Yang
Keyword(s):  
Singular Integral ◽  
Maximal Operator ◽  
Weak Type ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Operators ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Littlewood Maximal Operator

WeightedLpforp∈(1,∞)and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. All results with no weight on spaces of homogeneous type are also new.

Boundedness of operators of Hardy type in ΛP,q spaces and weighted mixed inequalities for singular integral operators

1997 ◽  
Vol 127 (1) ◽  
pp. 157-170 ◽  
Author(s):  
F. J. Martín-Reyes ◽  
P. Ortega Salvador ◽  
M. D. Sarrión Gavilán
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Weak Type ◽  
Integral Operators ◽  
Lorentz Spaces ◽  
Singular Integral Operators ◽  
Hardy Type

We consider certain n-dimensional operators of Hardy type and we study their boundedness in These spaces were introduced by M. J. Carro and J. Soria and include weighted Lp, q spaces and classical Lorentz spaces. As an application, we obtain mixed weak-type inequalities for Calderón—Zygmund singular integrals, improving results due to K. Andersen and B. Muckenhoupt.

scholarly journals Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Pu Zhang ◽  
Daiqing Zhang
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Lipschitz Condition ◽  
Singular Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Multilinear Commutator

LetTbe a singular integral operator with its kernel satisfying|K(x-y)-∑k=1ℓ‍Bk(x)ϕk(y)|≤C|y|γ/|x-y|n+γ,|x|>2|y|>0, whereBkandϕk  (k=1,…,ℓ)are appropriate functions andγandCare positive constants. Forb→=(b1,…,bm)withbj∈BMO(ℝn), the multilinear commutatorTb→generated byTandb→is formally defined byTb→f(x)=∫ℝn∏j=1m‍(bj(x)-bj(y))K(x,y)f(y)dy. In this paper, the weightedLp-boundedness and the weighted weak typeLlog⁡Lestimate for the multilinear commutatorTb→are established.

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