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The boundedness of the maximal Bochner-Riesz operator on $$L^ 4$$($$R^ 2$$). (English) Zbl 0522.42015

##### MSC:
 42B25 Maximal functions, Littlewood-Paley theory 42B15 Multipliers for harmonic analysis in several variables
##### Keywords:
maximal operator; multiplier; square functions
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##### References:
 [1] L. Carleson and P. Sjölin, Oscillatory integrals and a multiplier problem for the disc , Studia Math. 44 (1972), 287-299. (errata insert). · Zbl 0215.18303 · eudml:217689 [2] A. Córdoba, The multiplier problem for the polygon , Ann. of Math. (2) 105 (1977), no. 3, 581-588. JSTOR: · Zbl 0361.42005 · doi:10.2307/1970926 · links.jstor.org [3] A. Córdoba, A note on Bochner-Riesz operators , Duke Math. J. 46 (1979), no. 3, 505-511. · Zbl 0438.42013 · doi:10.1215/S0012-7094-79-04625-8 [4] A. Córdoba, Some remarks on the Littlewood-Paley theory , Rend. Circ. Mat. Palermo (2) (1981), no. suppl. 1, 75-80. · Zbl 0506.42022 [5] A. Córdoba and B. López-Melero, Spherical summation: a problem of E. M. Stein , Ann. Inst. Fourier (Grenoble) 31 (1981), no. 3, x, 147-152. · Zbl 0464.42006 · doi:10.5802/aif.842 · numdam:AIF_1981__31_3_147_0 · eudml:74501 [6] S. Igari, Decomposition theorem and lacunary convergence of Riesz-Bochner means of Fourier transforms of two variables , Tôhoku Math. J. (2) 33 (1981), no. 3, 413-419. · Zbl 0467.42017 · doi:10.2748/tmj/1178229404 [7] E. M. Stein, Some problems in harmonic analysis , Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978), Part 1, Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 3-20. · Zbl 0445.42006 [8] E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces , Princeton University Press, Princeton, N.J., 1971. · Zbl 0232.42007
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