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Zeitschrift für Analysis und ihre Anwendungen


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Volume 3, Issue 2, 1984, pp. 153–166
DOI: 10.4171/ZAA/97

Published online: 1984-04-30

Maximal inequalities and Fourier multipliers for spaces with mixed quasinorms. Applications

Hans-Jürgen Schmeisser[1]

(1) Friedrich-Schiller-University, Jena, Germany

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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Schmeisser Hans-Jürgen: Maximal inequalities and Fourier multipliers for spaces with mixed quasinorms. Applications. Z. Anal. Anwend. 3 (1984), 153-166. doi: 10.4171/ZAA/97