Octonion Fourier transform of Lipschitz real-valued functions of three variables on the octonion algebra

Abstract

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).