Borderline weak-type estimates for singular integrals and square functions

Carlos Domingo-Salazar, Michael Lacey, Guillermo Rey

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)63-73
Number of pages11
JournalBulletin of the London Mathematical Society
Volume48
Issue number1
DOIs
StatePublished - Feb 25 2015

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