In this article we discuss the behaviour of Θ-means of Walsh—Fourier series of a function in dyadic Hardy spaces H_p and dyadic homogeneous Banach spaces X. Namely, we estimate the rate of the approximation by Θ-means in terms of modulus of continuity in X and best approximation in H_p. Our main theorem is a generalization of a result of Fridli, Manchanda and Siddiqi [7]. Moreover, it extends a previous result of the authors [3]

中文翻译：

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在二元Hardy空间和二元齐次Banach空间中Walsh-Fourier级数的Θ-Means逼近

在本文中，我们讨论二元Hardy空间H _p和二元齐次Banach空间X中Walsh-Fourier级数的θ-均值的行为。即，我们根据X的连续模量和H _p的最佳逼近度来估计Θ-均值的逼近率。我们的主要定理是Fridli，Manchanda和Siddiqi [7]的结果的推广。此外，它扩展了作者的先前结果[3]。