Averaging and orthogonal operators on variable exponent spaces L-p(.) (Omega)
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2014
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Elsevier
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Hernández Rodríguez, F. L. & Ruiz Bermejo, C. «Averaging and Orthogonal Operators on Variable Exponent Spaces L p ( ⋅ ) ( Ω )». Journal of Mathematical Analysis and Applications, vol. 413, n.o 1, mayo de 2014, pp. 139-53. DOI.org (Crossref), https://doi.org/10.1016/j.jmaa.2013.11.048.
Abstract
Given a measurable space (Omega, mu) and a sequence of disjoint measurable subsets A = (A(n))(n), the associated averaging projection P-A and the orthogonal projection T-A are considered. We study the boundedness of these operators on variable exponent spaces L-P(.) (Omega). These operators are unbounded in general. Sufficient conditions on the sequence A in order to achieve that P-A or T-A be bounded are given. Conditions which provide the boundedness of P-A imply that T-A is also bounded. The converse is not true. Some applications are given. In particular, we obtain a sufficient condition for the boundedness of the Hardy-Littlewood maximal operator on spaces L-P(.) (Omega).
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Corrigendum to “Averaging and orthogonal operators on variable exponent spaces Lp(·) (Ω)” [J. Math. Anal. Appl. 413 (1) (2014)139–153]