Definition and Properties of the Libera Operator on Mixed Norm Spaces
We consider the action of the operator ℒg(z)=(1-z)-1∫z1f(ζ)dζ on a class of “mixed norm” spaces of analytic functions on the unit disk, X=Hα,νp,q, defined by the requirement g∈X⇔r↦(1-r)αMp(r,g(ν))∈Lq([0,1],dr/(1-r)), where 1≤p≤∞, 0<q≤∞, α>0, and ν is a nonnegative integer. This class contains...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/590656 |