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An inequality of the Hölder type, connected with Stieltjes integration. (English) Zbl 0016.10404

Keywords:
Analysis
References:
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[2]Bohr, H.: The arithmetic and geometric means, Journ. London Math. Soc. 10 (1935) 114. · Zbl 0011.34204 · doi:10.1112/jlms/s1-10.1.114
[3]Hardy, G. H.: Weierstrass’s non differentiable function, Trans. Amer. Math. Soc. 17 (1916), 301–325.
[4]Hardy, G. H. andLittlewood, J. E.: A convergence criterion for Fourier series, Math. Zeitschrift 28 (1928) 612–634. · Zbl 02576570 · doi:10.1007/BF01181186
[5]Hardy, G. H., Littlewood, J. E., andPólya, G.: Inequalities, Cambridge 1934.
[6]Helly, E.: Über lineare Funktionaloperationen, Wiener Sitzungsberichte 121 (1912), p. 265.
[7]Kogbetliantz, E.: Les séries trigonométriques et les séries sphériques, Annales Sc. de l’Ecole Normale (3) 40 (1923) 259–323.
[8]Kuttner, B.: A theorem on trigonometric series, Journ. London Math. Soc. 10 (1935) 131–135. · Zbl 0011.25501 · doi:10.1112/jlms/s1-10.1.131
[9]Pollard, S.: The Stieltjes integral and its generalisations, Quart. Journ. of Math. 49 (1923) 73–138.
[10]Pollard, S. andYoung, R. C.: On the integral a b dF(t) x-t, , Proc. London Math. Soc. (2) 28 (1928) 293–300. · doi:10.1112/plms/s2-28.1.145
[11]Wiener, N.: The Quadratic Variation of a function and its Fourier coefficients, Journ. Mass. Inst. of Technology 3 (1924) 73–94.
[12]Zygmund, A.: Trigonometrical series, Warsaw (1935).