Journal of Prime Research in Mathematics

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

Alexander Meskhi
Department of Mathematical Analysis, I. Javakhishvili Tbilisi State University,
Tbilisi, Georgia,
Abdus Salam School of Mathematical Sciences, GC University, 68-B New Muslim Town,
Lahore, Pakistan.
Ghulam Murtaza
Department of Applied Sciences, National Textile University, Faisalabad, Pakistan.

\(^{1}\)Corresponding Author:


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.


Riemann–Liouville discrete transform with product kernels, discrete Hardy operator, discrete potentials, weighted inequality, trace inequality.