正弦级数L^(1)可积性与Móricz结果

ON L^(1) INTEGRABILITY OF SINE SERIES AND MORICZ RESULT

本文建立了正弦级数(S_T)的例子,系数α_n→0,{α_n}∈(?)∩(?),但{α_n}(?),以及指出存在(S_T),α_n→0,{α_n}∈(?),‖S_n-g‖_1→0,但α_nIogn不趋于零。

An example of sine series S_T=sum from n=1 to ∞ α_n sin(nx) is established, where the coefficients α_n→0, {α_n}∈∩. but {α_n}. We show also that there exists such a (S_T), α_n→0, {α_n}∈(?), ‖S_n-g‖_1→0, but α_n Iogn does not approach to zero.