Choquet Integrals, Hausdorff Content and the Hardy-Littlewood Maximal Operator |
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Authors: | Orobitg Joan; Verdera Joan |
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Institution: | Departament de Matematiques, Universitat Antònoma de Barcelona 08193 Bellaterra (Barcelona), Spain |
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Abstract: | Using the BMO-H1 duality (among other things), D. R. Adams provedin 1] the strong type inequality
whereC is some positive constant independent of f. Here M is theHardyLittlewood maximal operator in Rn, H is the -dimensionalHausdorff content, and the integrals are taken in the Choquetsense. The Choquet integral of 0 with respect to a set functionC is defined by
Precise definitionsof M and H will be given below. For an application of (1) tothe Sobolev space W1, 1 (Rn), see 1, p. 114]. The purpose of this note is to provide a self-contained, directproof of a result more general than (1). 1991 Mathematics SubjectClassification 28A12, 28A25, 42B25. |
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