Abstract.
The authors prove L p bounds in the range 1<p<∞ for a maximal dyadic sum operator on R n. This maximal operator provides a discrete multidimensional model of Carleson’s operator. Its boundedness is obtained by a simple twist of the proof of Carleson’s theorem given by Lacey and Thiele [7] adapted in higher dimensions [9]. In dimension one, the L p boundedness of this maximal dyadic sum implies in particular an alternative proof of Hunt’s extension [4] of Carleson’s theorem on almost everywhere convergence of Fourier integrals.
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Mathematics Subject Classification (2000):Primary 42A20, Secondary 42A24
Grafakos is supported by the NSF. Tao is a Clay Prize Fellow and is supported by a grant from the Packard Foundation.
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Grafakos, L., Tao, T. & Terwilleger, E. L p bounds for a maximal dyadic sum operator. Math. Z. 246, 321–337 (2004). https://doi.org/10.1007/s00209-003-0601-4
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DOI: https://doi.org/10.1007/s00209-003-0601-4