Let \(n_j\) be a lacunary sequence of integers, such that \(n_{j+1}/n_j\ge r\). We are interested in linear combinations of the sequence of finite Riesz products \(\prod _{j=1}^N(1+\cos (n_j t))\). We prove that, whenever the Riesz products are normalized in \(L^p\) norm (\(p\ge 1\)) and when r is large enough, the \(L^p\) norm of such a linear combination is equivalent to the \(\ell ^p\) norm of the sequence of coefficients. In other words, one can describe many ways of embedding \(\ell ^p\) into \(L^p\) based on Fourier coefficients. This generalizes to vector valued \(L^p\) spaces.

令\（n_j \）为整数的舍弃序列，使得\（n_ {j + 1} / n_j \ ge r \）。我们对有限Riesz积\（\ prod _ {j = 1} ^ N（1+ \ cos（n_j t））\）的序列的线性组合感兴趣。我们证明，只要将Riesz乘积以\（L ^ p \）范数（\（p \ ge 1 \））进行归一化，并且当r足够大时，这种线性组合的\（L ^ p \）范数等效于系数序列的\（\ ell ^ p \）范数。换句话说，可以基于傅立叶系数描述将\（\ ell ^ p \）嵌入\（L ^ p \）的多种方法。这概括为向量值\（L ^ p \）空格。