A planar face on the unit sphere of the multiplier space $M_{p}$, $1<p<\infty$
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- by Charles Fefferman and Harold S. Shapiro PDF
- Proc. Amer. Math. Soc. 36 (1972), 435-439 Request permission
Abstract:
The unit sphere of the Banach space ${M_p}$ of Fourier multipliers, $1 < p < \infty$, is shown to contain a flat portion, i.e. a portion of a plane having codimension one. The proof is based on an elementary inequality, a generalization of the classical Bernoulli inequality.References
- R. E. Edwards, Fourier series: a modern introduction. Vol. II, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1967. MR 0222538 L. Leindler, On a generalization of Bernoulli’s inequality, Acta Sci. Math. (Szeged) (to appear).
- D. S. Mitrinović, Analytic inequalities, Die Grundlehren der mathematischen Wissenschaften, Band 165, Springer-Verlag, New York-Berlin, 1970. In cooperation with P. M. Vasić. MR 0274686
- Harold S. Shapiro, Fourier multipliers whose multiplier norm is an attained value, Linear operators and approximation (Proc. Conf., Math. Res. Inst., Oberwolfach, 1971) Internat. Ser. Numer. Math., Vol. 20, Birkhäuser, Basel, 1972, pp. 338–347. MR 0390623
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 435-439
- MSC: Primary 42A18
- DOI: https://doi.org/10.1090/S0002-9939-1972-0308669-X
- MathSciNet review: 0308669