Integral convolution operators
Copyright policy )Integral convolution operators
Let \(E_ 1,E_ 2\) and \(E_ 3\) be symmetric function spaces on an interval [0,a]. The following problem is under investigation: under which conditions is the convolution operator continuous from \(E_ 1\times E_ 2\) into \(E_ 3?\) The author gives some sufficient conditions for the continuity in terms of the Boyd indices \(\alpha_ E\) and \(\beta_ E\) of a space E. For example, if \(\beta_{E_ 3}+\beta_{E_ 1}1\), then the convolution operator maps \(E_ 1\times E_ 2\) continuously into \(E_ 3\).
Integral, integro-differential, and pseudodifferential operators, Convolution as an integral transform, convolution operator, sufficient conditions for the continuity in terms of the Boyd indices, symmetric function spaces on an interval, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Integral, integro-differential, and pseudodifferential operators, Convolution as an integral transform, convolution operator, sufficient conditions for the continuity in terms of the Boyd indices, symmetric function spaces on an interval, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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