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On a measure of non–compactness for maximal operators

✍ Scribed by D. E. Edmunds; A. Meskhi

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
146 KB
Volume
254-255
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

It is proved that there is no weight pair (v,w) for which the Hardy–Littlewood maximal operator defined on a domain Ω in R^n^ is compact from the weighted Lebesgue space L^p^~w~(Ω) to L^p^~v~ (Ω). Results of a similar character are also obtained for the fractional maximal operators. Moreover, a measure of non–compactness for these maximal operators is estimated from below. Analogous problems for one–sided maximal functions are also studied.

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