CONVOLUTION INEQUALITIES IN WEIGHTED LORENTZ SPACES: CASE 0 < q < 1

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10372624" target="_blank" >RIV/00216208:11320/17:10372624 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.7153/mia-20-13" target="_blank" >http://dx.doi.org/10.7153/mia-20-13</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7153/mia-20-13" target="_blank" >10.7153/mia-20-13</a>

Result language
angličtina
Original language name
CONVOLUTION INEQUALITIES IN WEIGHTED LORENTZ SPACES: CASE 0 < q < 1
Original language description
Let g be a fixed nonnegative radially decreasing kernel g. In this paper, boundedness of the convolution operator T(g)f := f*g between the weighted Lorentz spaces Gamma(q)(w) and Lambda(p)(v) is characterized in the case 0 < q < 1. The conditions are sufficient if the kernel g is just a general measurable function. Furthermore, the largest rearrangement-invariant (quasi-)space Y is found such that the Young-type inequality parallel to f*g parallel to(Gamma q(w)) <= C parallel to f parallel to (Lambda p(v))parallel to g parallel to Y holds for all f is an element of Lambda(p)(v) and g is an element of Y.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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