Optimal estimates for the Hardy averaging operator

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F10%3A00164774" target="_blank" >RIV/68407700:21110/10:00164774 - isvavai.cz</a>

Alternative codes found

RIV/00216208:11320/10:10057584

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Optimal estimates for the Hardy averaging operator

Original language description

Let Af(x) := 1/xint_0^x f(t) dt be the one-dimensional Hardy averaging operator. It is well-known that A is bounded on Lp whenever 1 < p =< inf.. We improve this result in the following sense: we introduce a pair of new function spaces, the 'source' space Sp, which is strictly larger than Lp, and the 'target' space Tp, which is strictly smaller than Lp, and prove that A is bounded from Sp into Tp. 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 Lp(x).

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2010

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematische Nachrichten

ISSN

0025-584X

e-ISSN

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Volume of the periodical

283

Issue of the periodical within the volume

2

Country of publishing house

DE - GERMANY

Number of pages

10

Pages from-to

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UT code for WoS article

000275649300007

EID of the result in the Scopus database

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