Lp theory for outer measures and two themes of Lennart Carleson united
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We develop a theory of Lp spaces based on outer measures rather than measures. This theory includes the classical Lp theory on measure spaces as special case. It also covers parts of potential theory and Carleson embedding theorems. The theory turns out to be an elegant language to describe aspects of classical singular integral theory such as paraproduct estimates and T(1) theorems, and it is particularly useful for generalizations of singular integral theory in time-frequency analysis. We formulate and prove a generalized Carleson embedding theorem and give a relatively short reduction of basic estimates for the bilinear Hilbert transform to this new Carleson embedding theorem.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/253be0bd3e412366a8e8d7f3bf481a3a2ef7abda
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In Applied Mathematics
Citations in the corpus
- Sharp commutator estimates via harmonic extensions (2016, background): “ons of trace characterizations of function (harmonically or otherwise) extended to the upper half-space. We are going to use probably the most classical one, the tent spaces and Carleson measures. In [23] they introduce “outer Lp-spaces, which might also offer a way to deal with the traces. A.1 The ”