In this paper, we examine the order of magnitude of the octonion Fourier transform (OFT) for real-valued functions of three variables and satisfiying certain Lipschitz conditions. In addition, using the analog of the operator Steklov, we construct the generalized modulus of smoothness, and also using the Laplacian operator we define the K-functional. We use the octonion Fourier transform (OFT) of real-valued functions of three variables to prove the equivalence between K-functionals and modulus of smoothness in the space of square-integrable functions (in Lebesgue sense).

中文翻译：

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octonion代数上三个变量的Lipschitz实值函数的Octonion Fourier变换

在本文中，我们针对三个变量的实值函数并满足某些Lipschitz条件，研究了八阶傅立叶变换（OFT）的量级。另外，使用算子Steklov的类似物，我们构造了广义的平滑模量，并且还使用了Laplacian算子，我们定义了K-泛函。我们使用三个变量的实值函数的正辛傅里叶变换（OFT）证明了在平方可积函数的空间中（Lebesgue的意义）K函数和光滑模量之间的等价关系。