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A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderon-Zygmund decomposition

Xavier Tolsa
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Abstract

Given a doubling measure $μ$ on $R^d$, it is a classical result of harmonic analysis that Calderon-Zygmund operators which are bounded in $L^2(μ)$ are also of weak type (1,1). Recently it has been shown that the same result holds if one substitutes the doubling condition on $μ$ by a mild growth condition on $μ$. In this paper another proof of this result is given. The proof is very close in spirit to the classical argument for doubling measures and it is based on a new Calderon-Zygmund decomposition adapted to the non doubling situation.

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Xavier Tolsa. 2000-02-25. A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderon-Zygmund decomposition. https://arxiv.org/abs/math/0002221

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