Sharp inclusions and lacunary series in mixed-norm spaces on the polydisc

Author： Avetisyan K.L.  

Publisher： Taylor & Francis Ltd

ISSN： 1747-6933

Source： Complex Variables and Elliptic Equations, Vol.58, Iss.2, 2013-02, pp. : 185-195

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Abstract

We establish the sharpness and strictness of continuous inclusions in mixed-norm spaces of n-harmonic functions on the unit polydisc of n . To this end, we modify a wellknown counterexample of Hardy and Littlewood and give a characterization of lacunary series with Hadamard gaps in mixed-norm and weighted Hardy spaces.

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