On Templeman averages and variation functions

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F12%3AA130168U" target="_blank" >RIV/61988987:17310/12:A130168U - 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

On Templeman averages and variation functions

Original language description

Let S be a countable semigroup acting in a measure-preserving fashion (g ? T g ) on a measure space (?, A, ?). For a finite subset A of S, let |A| denote its cardinality. Let (A k ) k=1 ? be a sequence of subsets of S satisfying conditions related to those in the ergodic theorem for semi-group actions of A. A. Tempelman. For A-measureable functions f on the measure space (?, A, ?) we form for k ? 1 the Templeman averages ?k(f)(x)=|Ak|?1?g?AkTgf(x) and set V q f(x) = (? k?1|? k+1(f)(x) ? ? k (f)(x)|q)1/qwhen q ? (1, 2]. We show that there exists C > 0 such that for all f in L 1(?, A, ?) we have ?({x ? ?: V q f(x) > ?}) ? C(?? | f | d?/?). Finally, some concrete examples are constructed.

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

2012

Confidentiality

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

Name of the periodical

Periodica Mathematica Hungarica

ISSN

0031-5303

e-ISSN

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Volume of the periodical

64

Issue of the periodical within the volume

1

Country of publishing house

HU - HUNGARY

Number of pages

13

Pages from-to

39-51

UT code for WoS article

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EID of the result in the Scopus database

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