Optimal estimates for the Hardy averaging operator | Zendy

Nekvinda Aleš | Zendy; Pick Luboš | Zendy

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Optimal estimates for the Hardy averaging operator

Author(s) -

Nekvinda Aleš,

Pick Luboš

Publication year - 2010

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200711155

Subject(s) - mathematics , lp space , bounded function , hardy space , banach space , standard probability space , operator (biology) , bounded operator , exponent , pure mathematics , space (punctuation) , discrete mathematics , mathematical analysis , computer science , biochemistry , chemistry , linguistics , philosophy , repressor , transcription factor , gene , operating system

Let be the one‐dimensional Hardy averaging operator. It is well‐known that A is bounded on L p whenever 1 < p ≤ ∞. We improve this result in the following sense: we introduce a pair of new function spaces, the ‘source’ space S p , which is strictly larger than L p , and the ‘target’ space T p , which is strictly smaller than L p , and prove that A is bounded from S p into T p . Moreover, we show that this result cannot be improved within the environment of solid Banach spaces. We present applications of this result to variable‐exponent Lebesgue spaces L p ( x ) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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