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

Authors

  • 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.

Keywords:

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

Abstract

We establish necessary and sufficient conditions on a weight sequence vj∞j=1vjj∞=1 governing the boundedness for the Riemann-Liouville discrete transform IαIα from lp(N)lp(N) to lqvj(N)lvjq(N) (trace inequality), where 0<α<10<α<1. The derived conditions are of DD. Adams or Maz’ya–Verbitsky (pointwise) type.

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Published

2013-12-31

Issue

Vol. 9 No. 1 (2013): Journal of Prime Research in Mathematics

Section

Regular

How to Cite

Weight characterization of the boundedness for the riemann-liouville discrete transform. (2013). Journal of Prime Research in Mathematics, 9(1), . 34 – 50. https://jprm.sms.edu.pk/index.php/jprm/article/view/90