An inequality of the Hölder type, connected with Stieltjes integration

Acta Mathematica - Tập 67 - Trang 251-282 - 1936
L. C. Young1
1Cambridge, England

Tài liệu tham khảo

Besicovitch, A. S.: Sur la nature des fonctions à carré sommable et des ensembles mesurables, Fundamenta Math. 4 (1923) 172–195. Bohr, H.: The arithmetic and geometric means, Journ. London Math. Soc. 10 (1935) 114. Hardy, G. H.: Weierstrass's non differentiable function, Trans. Amer. Math. Soc. 17 (1916), 301–325. Hardy, G. H. andLittlewood, J. E.: A convergence criterion for Fourier series, Math. Zeitschrift 28 (1928) 612–634. Hardy, G. H., Littlewood, J. E., andPólya, G.: Inequalities, Cambridge 1934. Helly, E.: Über lineare Funktionaloperationen, Wiener Sitzungsberichte 121 (1912), p. 265. Kogbetliantz, E.: Les séries trigonométriques et les séries sphériques, Annales Sc. de l'Ecole Normale (3) 40 (1923) 259–323. Kuttner, B.: A theorem on trigonometric series, Journ. London Math. Soc. 10 (1935) 131–135. Pollard, S.: The Stieltjes integral and its generalisations, Quart. Journ. of Math. 49 (1923) 73–138. Pollard, S. andYoung, R. C.: On the integral\(\int\limits_a^b {\frac{{dF(t)}}{{x - t}},} \), Proc. London Math. Soc. (2) 28 (1928) 293–300. Wiener, N.: The Quadratic Variation of a function and its Fourier coefficients, Journ. Mass. Inst. of Technology 3 (1924) 73–94. Zygmund, A.: Trigonometrical series, Warsaw (1935).