Weak type estimates and Cotlar inequalities for Calderón-Zygmund operators in nonhomogeneous spaces

Details Weak type estimates and Cotlar inequalities for Calderón-Zygmund operators in nonhomogeneous spaces Weak type estimates and Cotlar inequalities for Calderón-Zygmund operators in nonhomogeneous spaces

1997-11-24

arxiv.org/abs/math/9711210v1

Mathematics

Functional Analysis

Scientific paper

In the paper we consider Calder\'{o}n-Zygmund operators in nonhomogeneous spaces. We are going to prove the analogs of classical results for homogeneous spaces. Namely, we prove that a Calder\'{o}n-Zygmund operator is of weak type if it is bounded in $L^2$. We also prove several versions of Cotlar's inequality for maximal singular operator. One version of Cotlar's inequality (a simpler one) is proved in Euclidean setting, another one in a more abstract setting when Besicovich covering lemma is not available. We obtain also the weak type of maximal singular operator from these inequalities.

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