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

I. Blahota; K. Nagy; M. Salim

doi:10.1007/s10476-021-0083-9

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

I. Blahota, K. Nagy, M. Salim

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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].

Original language	English
Pages (from-to)	285-309
Number of pages	25
Journal	Analysis Mathematica
Volume	47
Issue number	2
DOIs	https://doi.org/10.1007/s10476-021-0083-9
Publication status	Published - Jun 2021

Keywords

Fejér mean
Nörlund mean
Walsh group
Walsh system
Walsh—Fourier series
approximation
dyadic Hardy space
dyadic homogeneous Banach space
modulus of continuity
weighted mean
Θ-mean

ASJC Scopus subject areas

Analysis
Mathematics(all)

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10.1007/s10476-021-0083-9

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

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].",

keywords = "Fej{\'e}r mean, N{\"o}rlund mean, Walsh group, Walsh system, Walsh—Fourier series, approximation, dyadic Hardy space, dyadic homogeneous Banach space, modulus of continuity, weighted mean, Θ-mean",

author = "I. Blahota and K. Nagy and M. Salim",

note = "Funding Information: This research was supported by project UAEU UPAR 2017 Grant G00002599. Publisher Copyright: {\textcopyright} 2021, Akad{\'e}miai Kiad{\'o}, Budapest.",

year = "2021",

month = jun,

doi = "10.1007/s10476-021-0083-9",

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journal = "Analysis Mathematica",

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T1 - Approximation by Θ-Means of Walsh—Fourier Series in Dyadic Hardy Spaces and Dyadic Homogeneous Banach Spaces

AU - Blahota, I.

AU - Nagy, K.

AU - Salim, M.

PY - 2021/6

Y1 - 2021/6

N2 - 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].

AB - 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].

KW - Fejér mean

KW - Nörlund mean

KW - Walsh group

KW - Walsh system

KW - Walsh—Fourier series

KW - approximation

KW - dyadic Hardy space

KW - dyadic homogeneous Banach space

KW - modulus of continuity

KW - weighted mean

KW - Θ-mean

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DO - 10.1007/s10476-021-0083-9

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JO - Analysis Mathematica

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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