Abstract
The paper concerns with maximal inequalities and Fourier multipliers for systems of entire analytic functions of exponential type belonging to mixed quasinormed spaces. As an application 4 types of spaces of functions with dominating mixed smoothness properties are introduced. Relations to classical spaces of that type (spaces of S.M. Nikol’skij, T.I. Amanov, P.I. Lizorkin) are treated. As a special case the Sobolev spaces with a dominating mixed derivative are contained.
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