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Weight characterization of the boundedness for the riemann-liouville discrete transform

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Title: Weight characterization of the boundedness for the riemann-liouville discrete transform

Authors: Alexander Meskhi, Ghulam Murtaza

Journal: Journal of Prime Research in Mathematics

HEC Recognition History
Category From To
Y 2023-07-01 2024-09-30
Y 2022-07-01 2023-06-30
Y 2021-07-01 2022-06-30
Y 2020-07-01 2021-06-30

Publisher: Abdus Salam School of Mathematical Sciences, GC University

Country: Pakistan

Year: 2013

Volume: 1

Issue: 1

Language: English

Keywords: Riemann-Liouville discrete transformweight sequenceboundedness

Categories
Fourier Analysis (7) Transforms (1) Analysis (236) Functional Analysis (104) Mathematics (5170)

Abstract

We establish necessary and sufficient conditions on a weight sequence \({v_j}^{∞}_{j}=1\) governing the boundedness for the Riemann-Liouville discrete transform \(I_α\) from \(l^p (\mathbb{N})\) to \(l^{q}_{vj}(N)\) (trace inequality), where \(0 < α < 1\). The derived conditions are of \(D\). Adams or Maz’ya–Verbitsky (pointwise) type.

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