This article is cited in 8 papers

The Hardy-Littlewood theorem for the cosine series in a symmetric space

V. A. Rodin

Voronezh State Pedagogical Institute

Abstract: For a wide class of functional spaces we obtain a necessary and sufficient condition on a space that guarantees a Hardy–Littlewood type of assertion about whether the sum of a cosine series with monotonic coefficients belongs to a functional space, e.g., $L_p$ ($p>1$). As examples we consider Lorentz spaces, Marcinkiewicz spaces, Orlicz spaces, and $L_p$ spaces.

UDC: 517.5

Received: 18.10.1974

 English version: Mathematical Notes, 1976, 20:2, 693–696

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