TY - JOUR
T1 - Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
AU - Lerner, Andrei K.
AU - Ombrosi, Sheldy
AU - Pérez, Carlos
PY - 2009/6
Y1 - 2009/6
N2 - A well-known open problem of Muckenhoupt-Wheeden says that any Calderón-Zygmund singular integral operator T is of weak type (1,1) with respect to a couple of weights (w,Mw). In this paper, we consider a somewhat "dual" problem: supλ > 0 λ w {x ∈ ℝn: |Tf(x)|/Mw > λ} ≤ c ∫ℝn |f|,dx. We prove a weaker version of this inequality with M 3 w instead of Mw. Also we study a related question about the behavior of the constant in terms of the A 1 characteristic of w.
AB - A well-known open problem of Muckenhoupt-Wheeden says that any Calderón-Zygmund singular integral operator T is of weak type (1,1) with respect to a couple of weights (w,Mw). In this paper, we consider a somewhat "dual" problem: supλ > 0 λ w {x ∈ ℝn: |Tf(x)|/Mw > λ} ≤ c ∫ℝn |f|,dx. We prove a weaker version of this inequality with M 3 w instead of Mw. Also we study a related question about the behavior of the constant in terms of the A 1 characteristic of w.
KW - Calderón-Zygmund operators
KW - Weights
UR - http://www.scopus.com/inward/record.url?scp=67650662452&partnerID=8YFLogxK
U2 - 10.1007/s00041-008-9032-2
DO - 10.1007/s00041-008-9032-2
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SN - 1069-5869
VL - 15
SP - 394
EP - 403
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
IS - 3
ER -