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Boundedness of strong means of Cesàro means on \(H^ p(\Sigma_ n)(0<p<1)\). (Chinese. English summary) Zbl 0727.42010

Summary: The method of atomatic decomposition is used to set up an estimate of boundedness of maximum strong means of Cesàro means at critical index on \(H^ p(\Sigma_ n)\) \((0<p<1):\) \[ \sup_{L>1}\{\frac{1}{\log L}\sum^{L}_{k=1}\frac{1}{k}\| \sigma_ k^{\delta}f\|^ p_{L^ p(\Sigma_ n)}\}^{1/p}\leq C_ p\| f\|_{H^ p(\Sigma_ n)}. \]

MSC:

42B05 Fourier series and coefficients in several variables
42B30 \(H^p\)-spaces
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