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  • Author or Editor: E. Nursultanov x
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Abstract  

Pointwise convergence of double trigonometric Fourier series of functions in the Lebesgue space L p[0, 2π]2 was studied by M.I.Dyachenko. In this paper, we also consider the problems of the convergence of double Fourier series in Pringsheim's sense with respect to the trigonometric as well as the Walsh systems of functions in the Lebesgue space L P[0, 1]2, p=(p 1, p 2), endowed with a mixed norm, in the particular case when the coefficients of the series in question are monotone with respect to each of the indices. We shall obtain theorems which generalize those of M. I. Dyachenko to the case when p is a vector. We shall also show that our theorems in the case of trigonometric Fourier series are best possible.

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Abstract  

An interpolation method is introduced for anisotropic spaces which generalizes the method by D. L. Fernandez [4]. By means of this method, interpolation properties of Besov B σq and Lizorkin-Triebel F σq spaces are investigated. Among others, the completeness of the scale of these spaces is proved with respect to the considered interpolation method.

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