Abstract
In this article we discuss the behaviour of Θ-means of Walsh—Fourier series of a function in dyadic Hardy spaces Hp 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 Hp. 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]
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This research was supported by project UAEU UPAR 2017 Grant G00002599.
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Blahota, I., Nagy, K. & Salim, M. Approximation by Θ-Means of Walsh—Fourier Series in Dyadic Hardy Spaces and Dyadic Homogeneous Banach Spaces. Anal Math 47, 285–309 (2021). https://doi.org/10.1007/s10476-021-0083-9
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DOI: https://doi.org/10.1007/s10476-021-0083-9
Key words and phrases
- Walsh group
- Walsh system
- Walsh—Fourier series
- Nörlund mean
- weighted mean
- Fejér mean
- approximation
- modulus of continuity
- Θ-mean
- dyadic homogeneous Banach space
- dyadic Hardy space