On a measure of non–compactness for maximal operators
Copyright policy )On a measure of non–compactness for maximal operators
AbstractIt is proved that there is no weight pair (v,w) for which the Hardy–Littlewood maximal operator defined on a domain Ω in Rn is compact from the weighted Lebesgue space Lpw(Ω) to Lpv (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.
- University of Sussex United Kingdom
Maximal functions, Littlewood-Paley theory, Linear operators on function spaces (general), fractional maximal operator, compactness, one-sided maximal operator, weighted Lebesgue spaces, Hardy-Littlewood maximal operator
Maximal functions, Littlewood-Paley theory, Linear operators on function spaces (general), fractional maximal operator, compactness, one-sided maximal operator, weighted Lebesgue spaces, Hardy-Littlewood maximal operator
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