Imbedding theorems and convergence of multiple Fourier series (Q753087)

Using anisotropic fractional differences, spaces of type \(B^ r_{p,\infty}\) (with p and r vectors) are defined. Another class denoted by \(SH^{\alpha}_ p\) of similar type defined via mixed differences is considered and conditions on the indices are found for imbeddings with the latter spaces as a target. Applications are given to uniform convergence of the Fourier series of functions from the periodic version of the former spaces. The paper is directly linked with the paper of the author [Tr. Mat. Inst. Steklova 172, 60-70 (1985; Zbl 0576.39004)].