Pernecká, Pick: Compactness of Hardy Operators Involving Suprema

Pernecká, Eva and Pick, Luboš:
Compactness of Hardy Operators Involving Suprema
Bollettino dell'Unione Matematica Italiana Serie 9 6 (2013), fasc. n.1, p. 219-252, (English)
pdf (434 Kb), djvu (302 Kb). | MR 3086798 | Zbl 1294.47052

Sunto

We study compactness properties of Hardy operators involving suprema on weighted Banach function spaces. We first characterize the compactness of abstract operators assumed to have their range in the class of non-negative monotone functions. We then define a category of pairs of weighted Banach function spaces for which a suitable Muckenhoupt-type condition implies the boundedness of Hardy operators involving suprema, and prove a criterion for the compactness of these operators between such a couple of spaces. Finally, we characterize the compactness of these operators on weighted Lebesgue spaces including those which do not belong to the above-mentioned category.

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Referenze Bibliografiche