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

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dc.creatorTolsa, Xavier
dc.date2000-06-05
dc.date.accessioned2026-07-07T04:35:45Z
dc.date.available2026-07-07T04:35:45Z
dc.descriptionLet $μ$ 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 $0<n\leq d$. In this paper, we develop Littlewood-Paley theory for functions in $L^p(μ)$. One of the main difficulties is the construction of reasonable approximations of the identity for obtaining a Calderon type reproducing formula. Moreover, it is shown that the T(1) theorem for n-dimensional Calderon-Zygmund operators, without doubling assumptions, can be proved using the Littlewood-Paley decomposition that is obtained for $L^2(μ)$ functions, as in the classical case of homogeneous spaces.
dc.description47 pages
dc.identifierhttps://arxiv.org/abs/math/0006039
dc.identifierhttp://arxiv.org/abs/math/0006039
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59357
dc.subjectClassical Analysis and ODEs
dc.subjectFunctional Analysis
dc.subject42B20; 42B30
dc.titleLittlewood-Paley theory and the T(1) theorem with non doubling measures
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