The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F10%3A00342832" target="_blank" >RIV/67985840:_____/10:00342832 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
The averaging integral operator between weighted Lebesgue spaces and reverse Hölder inequalities
Original language description
Let 1 < p q < + and v, w be weights on (0, +) such that v(x)x? is equivalent to a non-decreasing function on (0, +) for some ? 0, and ... First, we prove that the operator ... if and only if the operator ... Second, we show that the boundedness of the averaging operator A on the space Lp((0, +); v) implies that, for all r > 0, the weight v1-p' satisfies the reverse Hlder inequality over the interval (0, r) with respect to the measure dt, while the weight v satisfies the reverse Hlder inequality over theinterval (r, +) with respect to the measure t-p dt. As a corollary, we obtain that the boundedness of the averaging operator A on the space Lp((0, +); v) is equivalent to the boundedness of the averaging operator A on the space Lp((0, +); v1+?) for some? > 0.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA201%2F08%2F0383" target="_blank" >GA201/08/0383: Function Spaces, Weighted Inequalities and Interpolation</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Complex Variables and Elliptic Equations. An International Journal
ISSN
1747-6933
e-ISSN
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Volume of the periodical
55
Issue of the periodical within the volume
8-10
Country of publishing house
GB - UNITED KINGDOM
Number of pages
8
Pages from-to
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UT code for WoS article
000282807200018
EID of the result in the Scopus database
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