Trigonometrical Series

a₁ a₂ absolute convergence absolute value apply arbitrary b₁ b₂ belongs bounded variation C₁ C₂ Clothbound completes the proof conjugate consider constant continuous function converges absolutely converges uniformly convex corollary deduce defined denote diverges equal exceed exists f is continuous f₁ Fatou's lemma Fejér finite number formula Fourier coefficients Fourier series func function f(x Hardy and Littlewood Hence Hölder's inequality integral of f interval kernel Lebesgue left-hand side Let f Let F(x linear mean-value theorem necessary and sufficient non-decreasing non-negative observe obtain on(x P₁ Paperbound Parseval's relation partial sums polynomial prove result Riesz Riesz-Fischer theorem satisfies sequence set of points Sn(x sufficient condition summable suppose tends uniformly term theory tion total variation trigonometrical series uniformly bounded vanishes x₁ Zygmund