Borderline weak‐type estimates for singular integrals and square functions

By C. Domingo-Salazar, Michael T. Lacey, G. Rey. 2015

65 citations recorded by the source corpus.

For any Calderón–Zygmund operator T , any weight w , and α>1 , the operator T is bounded as a map from L1(MLloglogL(logloglogL)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(logL)ϵ scale. Also, for square functions Sf , 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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/b04454d9f57b1eebf333ceb8f6757f037a4e8832

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In Applied Mathematics

Citations in the corpus

On pointwise and weighted estimates for commutators of Calder\'on-Zygmund operators (2016, background): “Rey [9] obtained the following improvement of (1.”