TY  - BOOK
AU  - Blaimer,Bettina
TI  - Optimal domain and integral extension of operators acting in Frechet function spaces
SN  - 3832545573
AV  - Internet Access AEGMCT
U1  - 515.73 22
PY  - 2017///]
CY  - Berlin, Germany
PB  - Logos Verlag Berlin GmbH
KW  - Mathematics
KW  - Math�ematiques
KW  - bisacsh
KW  - fast
KW  - Electronic books
N1  - Includes bibliographical references and index
N2  - It is known that a continuous linear operator T defined on a Banach function space X(�I¼) (over a finite measure space ( Omega,§igma,�I¼)) and with values in a Banach space X can be extended to a sort of optimal domain. Indeed, under certain assumptions on the space X(�I¼) and the operator T this optimal domain coincides with L�A�(m�a T), the space of all functions integrable with respect to the vector measure m�a T associated with T, and the optimal extension of T turns out to be the integration operator I�a m�a T. In this book the idea is taken up and the corresponding theory is translated to a larger class of function spaces, namely to Fr�echet function spaces X(�I¼) (this time over a �I -finite measure space ( Omega,§igma,�I¼)). It is shown that under similar assumptions on X(�I¼) and T as in the case of Banach function spaces the so-called ``optimal extension process'' also works for this altered situation. In a further step the newly gained results are applied to four well-known operators defined on the Fr�echet function spaces L^p-([0,1]) resp. L^p-(G) (where G is a compact Abelian group) and L^p�a textloc( mathbbR)
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ER  -