X. Tolsa

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math.CA2002

Painleve's problem and the semiadditivity of analytic capacity

Xavier Tolsa

Let $γ (E)$ be the analytic capacity of a compact set $E$ and let $γ_{+} (E)$ be the capacity of $E$ originated by Cauchy transforms of positive measures. In this paper we prove that $…

math.CA2000

Littlewood-Paley theory and the T(1) theorem with non doubling measures

Xavier Tolsa

Let $μ$ be a Borel measure on $R^{d}$ which may be non doubling. The only condition that $μ$ must satisfy is $μ (B (x, r)) \leq C r^{n}$ for all $x \in R^{d}$ , $r > 0$ , and for some fixed $0<n\…

math.CA2000

Characterization of the atomic space $H^{1}$ for non doubling measures in terms of a grand maximal operator

Xavier Tolsa

Let $μ$ be a Radon measure on $R^{d}$ , which may be non doubling. The only condition that $μ$ must satisfy is $μ (B (x, r)) \leq C r^{n}$ , for all $x, r$ and for some fixed $0 < n \leq d$ . Rec…

math.CA2000

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

Xavier Tolsa

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). Rece…

math.CA2000

BMO, H^1, and Calderon-Zygmund operators for non doubling measures

Xavier Tolsa

Given a Radon measure $μ$ on $R^{d}$ , which may be non doubling, we introduce a space of type BMO with respect to this measure. It is shown that many properties that hold when $μ$ is…

Painleve's problem and the semiadditivity of analytic capacity

Littlewood-Paley theory and the T(1) theorem with non doubling measures

Characterization of the atomic space H1 for non doubling measures in terms of a grand maximal operator

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

BMO, H^1, and Calderon-Zygmund operators for non doubling measures

Characterization of the atomic space $H^{1}$ for non doubling measures in terms of a grand maximal operator