Research PaperNo Access

Existence of unconditional wavelet bases for $L^{p}$ -norm over a local fields of positive characteristic

Ashish Pathak

https://orcid.org/0000-0003-0143-7979

Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India

E-mail Address: ashishpathak@bhu.ac.in

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and

Dileep Kumar

Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India

E-mail Address: dkbhu07@gmail.com

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https://doi.org/10.1142/S021969132350008XCited by:1 (Source: Crossref)

Abstract

In this paper, we defined Calder $\overset{́}{o}$ n–Zygmund operator $T$ as $(T ϕ) (x) = \int_{𝕂} 𝒦 (x, y) ϕ (y) d y$ on local fields ( $𝕂$ ) under certain conditions on $𝒦 (x, y)$ and then find the boundedness of operator $T$ . Using result on boundedness of $T$ and orthonormal wavelet basis of $L^{2} (𝕂)$ , we provide unconditional wavelet bases for $L^{p}$ -norm over a local fields of positive characteristic by the wavelet coefficients.

Keywords:

AMSC: 42C40, 11F85, 42A38, 42B20

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