Nagel, Alexander; Vance, James; Wainger, Stephen; Weinberg, David Hilbert transforms for convex curves. (English) Zbl 0524.44001 Duke Math. J. 50, 735-744 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 40 Documents MSC: 44A15 Special integral transforms (Legendre, Hilbert, etc.) 42B15 Multipliers for harmonic analysis in several variables 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) Keywords:Lp-bounds; Hilbert transform; convex plane curves; Fourier transform PDF BibTeX XML Cite \textit{A. Nagel} et al., Duke Math. J. 50, 735--744 (1983; Zbl 0524.44001) Full Text: DOI References: [1] W. C. Nestlerode, Singular integrals and maximal functions associated with highly monotone curves , Trans. Amer. Math. Soc. 267 (1981), no. 2, 435-444. JSTOR: · Zbl 0488.42016 [2] A. Nagel, N. M. Rivière, and S. Wainger, On Hilbert transforms along curves. II , Amer. J. Math. 98 (1976), no. 2, 395-403. JSTOR: · Zbl 0334.44012 [3] A. Nagel, E. M. Stein, and S. Wainger, Hilbert transforms and maximal functions related to variable curves , 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. 95-98. · Zbl 0463.42008 [4] A. Nagel and S. Wainger, Hilbert transforms associated with plane curves , Trans. Amer. Math. Soc. 223 (1976), 235-252. · Zbl 0341.44005 [5] W. Rudin, Principles of mathematical analysis , Second edition, McGraw-Hill Book Co., New York, 1964. · Zbl 0148.02903 [6] E. M. Stein and S. Wainger, The estimation of an integral arising in multiplier transformations. , Studia Math. 35 (1970), 101-104. · Zbl 0202.12401 [7] E. M. Stein and S. Wainger, Problems in harmonic analysis related to curvature , Bull. Amer. Math. Soc. 84 (1978), no. 6, 1239-1295. · Zbl 0393.42010 [8] D. A. Weinberg, The Hilbert transform and maximal function for approximately homogeneous curves , Trans. Amer. Math. Soc. 267 (1981), no. 1, 295-306. · Zbl 0484.42005 [9] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II , Cambridge University Press, New York, 1959. · Zbl 0085.05601 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.