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Calderón-type theorems for operators with non-standard endpoint behavior on Lorentz spaces
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology. (Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic)
2012 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 285, no 11-12, 1450-1465 p.Article in journal (Refereed) Published
Abstract [en]

The Calderón theorem states that every quasilinear operator, which is bounded both from to , and from  to  for properly ordered values of , 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 Λ and M spaces will be the endpoints of the interpolation segment. Two distinctive types of non-standard behavior are to be discussed; we’ll explore the operators bounded both from Λ(X1) to Λ(Y1), and from Λ(X2) to M(Y2) using duality arguments, thus, we need to study the operators bounded both from Λ(X1) to M(Y1), and from M(X2) to M(Y2) first. For that purpose, we evaluate Peetre's K-functional for varied pairs of Lorentz spaces.

Place, publisher, year, edition, pages
Berlin, Germany: Wiley-VCH Verlagsgesellschaft, 2012. Vol. 285, no 11-12, 1450-1465 p.
Keyword [en]
Calderón theorem; Calderón operator; Interpolation of quasilinear operators; Lorentz spaces; msc (2010) Primary: 46B70; Secondary: 26D10
National Category
URN: urn:nbn:se:liu:diva-80786DOI: 10.1002/mana.201100095ISI: 000307008700012OAI: diva2:548266

Funding Agencies||SVV-2010-261316|

Available from: 2012-08-30 Created: 2012-08-30 Last updated: 2012-09-05Bibliographically approved

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Malý, Lukáš
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Mathematics and Applied MathematicsThe Institute of Technology
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