TY - JOUR
T1 - Borderline weak-type estimates for singular integrals and square functions
AU - Domingo-Salazar, Carlos
AU - Lacey, Michael
AU - Rey, Guillermo
N1 - Publisher Copyright:
© 2015 London Mathematical Society.
PY - 2015/2/25
Y1 - 2015/2/25
N2 - For any Calderón-Zygmund operator T, any weight w, and α >1, the operator T is bounded as a map from L1 (ML log log L (log log log L)αw) into weak-L1(w). The interest in questions of this type goes back to the beginnings of the weighted theory, with prior results, due to Coifman-Fefferman, Pérez, and Hytönen-Pérez, on the L (log L)ε scale. Also, for square functions S f, and weights w ∈ Ap, the norm of S from Lp(w) to weak-Lp(w), 2≤ p < ∞, is bounded by [w]Ap1/2 (1+log [w]A∞)1/2, which is a sharp estimate.
AB - For any Calderón-Zygmund operator T, any weight w, and α >1, the operator T is bounded as a map from L1 (ML log log L (log log log L)αw) into weak-L1(w). The interest in questions of this type goes back to the beginnings of the weighted theory, with prior results, due to Coifman-Fefferman, Pérez, and Hytönen-Pérez, on the L (log L)ε scale. Also, for square functions S f, and weights w ∈ Ap, the norm of S from Lp(w) to weak-Lp(w), 2≤ p < ∞, is bounded by [w]Ap1/2 (1+log [w]A∞)1/2, which is a sharp estimate.
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U2 - 10.1112/blms/bdv090
DO - 10.1112/blms/bdv090
M3 - Article
AN - SCOPUS:84962286010
VL - 48
SP - 63
EP - 73
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
SN - 0024-6093
IS - 1
ER -