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- W2979756876 abstract "We prove that the lacunary Carleson operator is bounded from LlogL to L1. This result is sharp. The proof is based on two newly introduced concepts: the time-frequency regularization of a measurable set and the set-resolution of the time-frequency plane at 0-frequency. Another key insight of our paper is that it provides for the first time a simultaneous treatment of families of tiles with distinct mass parameters. This should be regarded as a fundamental feature/difficulty of the problem of the pointwise convergence of Fourier Series near L1, context in which, unlike the standard Lp,p>1 case, no decay in the mass parameter is possible." @default.
- W2979756876 created "2019-10-18" @default.
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- W2979756876 date "2019-12-01" @default.
- W2979756876 modified "2023-10-14" @default.
- W2979756876 title "The pointwise convergence of Fourier Series (II). Strong L1 case for the lacunary Carleson operator" @default.
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- W2979756876 doi "https://doi.org/10.1016/j.aim.2019.106831" @default.
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