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- Publisher: eScholarship, University of California
- Journal: 457-497issn: 1016-443X
Related identifiers: doi: 10.1007/s00039-009-0010-x - Subject: Geometry and Topology | Mathematics | Time-frequency analysis | 42A99 | Mathematics - Classical Analysis and ODEs | quadratic phase | Analysis | Carleson’s theorem

We prove that the generalized Carleson operator with polynomial phase function of degree two is of weak type (2,2). For this, we introduce a new approach to the time-frequency analysis of the quadratic phase.

- References (12) 12 references, page 1 of 2
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Now, for x ∈ Ij fixed, we conclude that 1 B(x) sup I⊃Ij |I| I

1 + |2ξk| −n−2 (δ1/3dj,l)n|ξ|ndξ 1 + |2ξk| −n−2 dξ 2k(2kδ1/3dj,l)n .

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[S1] E.M. Stein, On limits of sequences of operators, Ann. of Math. 74 (1961), 140-170.

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