Calderón-type theorems for operators with non-standard endpoint behavior on Lorentz spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10127345" target="_blank" >RIV/00216208:11320/12:10127345 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/mana.201100095" target="_blank" >http://dx.doi.org/10.1002/mana.201100095</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.201100095" target="_blank" >10.1002/mana.201100095</a>

Result language
angličtina
Original language name
Calderón-type theorems for operators with non-standard endpoint behavior on Lorentz spaces
Original language description
The Calderón theorem states that every quasilinear operator, which is bounded both from $L^{p_1,1}$ to $L^{q_1,infty}$, and from $L^{p_2,1}$ to $L^{q_2,infty}$ for properly ordered values of $p_1$, $p_2$, $q_1$, $q_2$, is bounded on some rearrangement-invariant space if and only if the so-called Calderón operator is bounded on the corresponding representation space. We will establish Calderón-type theorems for non-standard endpoint behavior, where Lorentz $Lambda$ and $M$ spaces will be the endpointsof the interpolation segment. Two distinctive types of non-standard behavior are to be discussed; we'll explore the operators bounded both from $Lambda(X_1)$ to $Lambda(Y_1)$, and from $Lambda(X_2)$ to $M(Y_2)$ using duality arguments, thus, we needto study the operators bounded both from $Lambda(X_1)$ to $M(Y_1)$, and from $M(X_2)$ to $M(Y_2)$ first. For that purpose, we evaluate Peetre's $K$-functional for varied pairs of Lorentz spaces.
Czech name
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Czech description
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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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Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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