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Zeitschrift für Analysis und ihre Anwendungen

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Volume 21, Issue 3, 2002, pp. 681–690
DOI: 10.4171/ZAA/1102

Published online: 2002-09-30

Potential-Type Operators in $L^{p(x)}$ Spaces

David E. Edmunds[1] and Alexander Meskhi[2]

(1) University of Sussex, Brighton, United Kingdom
(2) Georgian Acadademy of Sciences, Tbilisi, Georgia

In this paper we derive weight inequalities for one-sided and Riesz potentials in $L^{p(x)}$ spaces under the condition that $p$ satisfies a weak Lipschitz condition. Compactness of these operators in $L^{p(x)}$ spaces is also established.

Keywords: Lebesgue spaces with variable exponent, Riemann–Liouville and Weyl operators, Riesz potentials

Edmunds David, Meskhi Alexander: Potential-Type Operators in $L^{p(x)}$ Spaces. Z. Anal. Anwend. 21 (2002), 681-690. doi: 10.4171/ZAA/1102