Weight characterization of the boundedness for the riemann-liouville discrete transform | [Journal of Prime Research in Mathematics • 2013]

Author(s):

1. 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.

2. GHULAM MURTAZA: Department of Applied Sciences, National Textile University,Faisalabad,Pakistan

Abstract:

We establish necessary and su±cient conditions on a weight sequence fvjgj1=1 governing the boundedness for the Riemann-Liouville discrete transform I® from lp(N) to lvqj (N) (trace inequality), where 0 < ® < 1. The derived conditions are of D. Adams or Maz'ya{Verbitsky (pointwise) type.

Page(s): 34-50

DOI: DOI not available

Published: Journal: Journal of Prime Research in Mathematics, Volume: 9, Issue: 1, Year: 2013

Keywords:

AMS SUBJECT , Secondary 47B38 , discrete potentials , Primary 26D15 , RiemannLiouville discrete transform with product kernels , weighted inequality , discrete Hardy operator , trace inequality , 46E30

References:

[1] Adams D. .1973 .A trace inequality for generalized potentials. Studia Math, 48 : 99-105.

[2] Edmunds D. E.,Kokilashvili V.,Meskhi A. .2002 .Bounded and compact integral operators. , : .

[3] Kokilashvili V.,Meskhi A. . .On a trace inequality for one-sided potentials and applications to the solvability of nonlinear integral equations. Georgian Math. J. 8, 3(2001) : 536.

[4] V. G. ,Verbitsky I. E. .1995 .Capacitary inequalities for fractional integrals, with applications to partial di®erential equations and Sobolev multipliers. Ark. Mat, 81 : 115.

[5] Meskhi A. . .Solution of some weight problems for the Riemann{Liouville and Weyl operators. Georgian Math. J. 5, 6(565) : 574.

[6] Meskhi A. .2001 .On the boundedness and compactness criteria for the Riemann{Liouville type discrete operator. Proc. A. Razmadze Math. Inst, 117 : 119.

[7] Prokhorov D. V. .2000 .On the boundedness of a class of integral operators. J. London Math. Soc, 2(617) : 628.

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