Averaging Operators on l^{p_n} and L^p(x)

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F02%3A00096013" target="_blank" >RIV/68407700:21110/02:00096013 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Averaging Operators on l^{p_n} and L^p(x)

Original language description

We consider the generalized Lebesgue space $L^{p(x)}$ and its discrete analogue $l^{{p_n}}$, each given the appropriate Luxemburg norm. Let $T_k$ be the averaging operator given by $$ (T_ka)_n=frac{1}{k}(a_n+a_{n+1}+ldots +a_{n+k-1}), a={a_n}in l^{{p_n}} $$ We show that the $T_k$ are uniformly bounded from $l^{{p_n}}$ into $l^{{p_n}}$ under certain assumptions on ${p_n}$ and find a counter-example to show that $T_k$ need not be bounded if these assumptions are not satisfied.

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

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2002

Confidentiality

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

Name of the periodical

Mathematical Inequalities and Applications

ISSN

1331-4343

e-ISSN

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Volume of the periodical

5

Issue of the periodical within the volume

2

Country of publishing house

HR - CROATIA

Number of pages

12

Pages from-to

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UT code for WoS article

000175630800009

EID of the result in the Scopus database

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