Integrability of trigonometric series. II

Masako Izumi and Shin-ichi Izumi

Vol. 42 (1972), No. 2, 359–367

DOI: 10.2140/pjm.1972.42.359

Abstract

There are proved theorems of the following type. Let 0 < r < 1 and g(t) ∼∑ _n=1^∞b_n sinnt and suppose ∫ ₀ⁿg(t)|t−u|^−rdt ≦ A for all u > 0. Then ∑ _n=1^∞|b_n|n^r−1 < ∞.

Mathematical Subject Classification 2000

Primary: 42A16

Secondary: 42A28

Milestones

Received: 1 April 1971

Published: 1 August 1972