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Averaging and orthogonal operators on variable exponent spaces L-p(.) (Omega)

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Hernández, Francisco L. and Ruiz Bermejo, César (2014) Averaging and orthogonal operators on variable exponent spaces L-p(.) (Omega). Journal of mathematical analysis and applications, 413 (1). pp. 139-153. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X13010597


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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).


Item Type:Article
Additional Information:

Corrigendum to “Averaging and orthogonal operators on variable exponent spaces Lp(·) (Ω)” [J. Math. Anal. Appl. 413 (1) (2014)139–153]

Uncontrolled Keywords:Variable exponent spaces; Bounded projections; Maximal operator
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:24702
Deposited On:17 Mar 2014 12:00
Last Modified:13 May 2016 11:14

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