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: meskhi@rmi.ge

### 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.

#### Keywords:

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