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Zeitschrift für Analysis und ihre Anwendungen

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Volume 26, Issue 2, 2007, pp. 179–193
DOI: 10.4171/ZAA/1317

Published online: 2007-06-30

Pointwise Inequalities in Variable Sobolev Spaces and Applications

Alexandre Almeida[1] and Stefan Samko[2]

(1) Universidade de Aveiro, Portugal
(2) University of Algarve, Faro, Portugal

Pointwise estimates for variable exponent Sobolev functions are derived to obtain several results on Sobolev spaces with variable exponent. Hypersingular operators acting in these spaces are considered and the corresponding boundedness and pointwise statements are given over bounded open sets with Lipschitz boundary. Moreover, classical Sobolev embeddings into H\"{o}lder spaces are generalized to the variable exponent setting.

Keywords: Variable exponent, Sobolev space, Sobolev embedding, Hölder space, variable order, maximal function, hypersingular integral

Almeida Alexandre, Samko Stefan: Pointwise Inequalities in Variable Sobolev Spaces and Applications. Z. Anal. Anwend. 26 (2007), 179-193. doi: 10.4171/ZAA/1317