Geodesic
Absolute Convergence Factors for Hp Series
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 187-195

Voir la notice de l'article provenant de la source Cambridge University Press

A famous theorem of Hardy asserts that if f ∊ H 1, then the sequence of Fourier coefficients satisfies . For this reason we say that the sequence (1, 1/2, 1/3, ...) belongs to the multiplier class (H1, l 1). In this paper, we investigate the multiplier classes (Hp , l 1) for 1 ≧ p ≧ ∞. Our observations are based on the fact that a sequence (λ(0), λ(l), ...) belongs to (Hp , l 1) independent of the arguments of its terms. We also show that (Hp , l 1) may be thought of as the conjugate space of a certain Banach space. 1. Preliminaries.Lp denotes the space of complex-valued Lebesgue measurable functions f defined on the circle |z| = 1 such that is finite. 
Caveny, James. Absolute Convergence Factors for Hp Series. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 187-195. doi: 10.4153/CJM-1969-018-9
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