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Approximation by Θ-Means of Walsh—Fourier Series in Dyadic Hardy Spaces and Dyadic Homogeneous Banach Spaces

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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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Authors and Affiliations

  1. Institute of Mathematics and Computer Sciences, University of Nyíregyháza, Nyíregyháza, Hungary

    I. Blahota

  2. Department of Mathematical Sciences, College of Science, UAEU, Al Ain, United Arab Emirates

    K. Nagy & M. Salim

  3. Institute of Mathematics and Computer Science, Eszterházy Károly University, Eger, Hungary

    K. Nagy

Authors
  1. I. Blahota
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  2. K. Nagy
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  3. M. Salim
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Correspondence to I. Blahota.

Additional information

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

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