Calderón–Zygmund decompositions in tent spaces and weak-type endpoint bounds for two quadratic functionals of Stein and Fefferman–Stein
Volume 239 / 2017
Studia Mathematica 239 (2017), 123-132
MSC: Primary 42B20, 42B35; Secondary 42B25.
DOI: 10.4064/sm8458-3-2017
Published online: 17 July 2017
Abstract
We prove some Calderón–Zygmund type decompositions for functions in the tent spaces introduced by Coifman, Meyer and Stein. These decompositions will be useful in the operator theory on tent spaces developed in the author’s 2015 thesis. As an application of these decompositions to the study of quadratic functionals on tent spaces, we give a unified proof for tent space generalizations of C. Fefferman’s endpoint weak-type estimates for grand square functions and of C. Fefferman and Stein’s endpoint weak-type estimates for box maximal functions.
