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Separable anisotropic differential operators in weighted abstract spaces and applications |
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| Authors: | Ravi P Agarwal Donal O'Regan |
| Institution: | a Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA b Department of Mathematics, National University of Ireland, Galway, Ireland c Istanbul University, Engineering Faculty, Department of Electrical-Electronics Engineering, Avcilar, 34320 Istanbul, Turkey |
| Abstract: | In this paper operator-valued multiplier theorems in Banach-valued weighted Lp spaces are studied. Also weighted Sobolev-Lions type spaces  are discussed when E0, E are two Banach spaces and E0 is continuously and densely embedded on E. Several conditions are found that ensure the continuity of the embedding operators that are optimally regular in these spaces in terms of interpolations of E0. These results permit us to show the separability of the anisotropic differential operators in an E-valued weighted Lp space. By using these results the maximal regularity of infinite systems of quasi elliptic partial differential equations are established. |
| Keywords: | Banach space-valued functions Operator-valued multipliers UMD spaces R-bounded sets Boundary value problems Differential-operator equations Interpolation of Banach spaces Positive operators |
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