二重三角级数和函数的范数研究

The Research for Dual Trigonometric Series

对形如 ∞n=0 ∞m=0amncosmxcosny等二重三角级数的和函数进行了研究 ,并证明了其范数‖f(x ,y)‖ p =∫π-π∫π-π｜f(x ,y) ｜p1dxp2 /p1dy1 /p2 <∞所满足的几个不等式 .

In this paper, we studied the sum function of dual trigonometric series form as ∞n=0∞m=0a_ mn cosmxcosny, and proved a few of inequalities related to norm of sum function ‖f(x,y)‖_ =∫~π_ -π ∫~π_ -π |f(x,y)|~ p_1 dx~ p_2/p_1 dy1/p_2<∞