Siberian Mathematical Journal

, Volume 54, Issue 2, pp 368–378

On boundedness and compactness of Riemann-Liouville fractional operators

Article

DOI: 10.1134/S0037446613020183

Cite this article as:
Farsani, S.M. Sib Math J (2013) 54: 368. doi:10.1134/S0037446613020183

Abstract

Let α ∈ (0, 1). Consider the Riemann-Liouville fractional operator of the form
$$f \to T_\alpha f(x): = v(x)\int\limits_0^x {\frac{{f(y)u(y)dy}} {{(x - y)^{1 - \alpha } }}} ,x > 0, $$
with locally integrable weight functions u and v. We find criteria for the LpLq-boundedness and compactness of Tα when 0 < p,q < ∞, p > 1/α under the condition that u monotonely decreases on ℝ+:= [0,∞). The dual versions of this result are given.

Keywords

Riemann-Liouville fractional operator Lebesgue space weighted inequality 

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.People’s Friendship University of RussiaMoscowRussia

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