Sum of weighted Lebesgue spaces and nonlinear elliptic equations |
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| Authors: | Marino Badiale Lorenzo Pisani Sergio Rolando |
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| Institution: | 1. Dipartimento di Matematica, Universit?? degli Studi di Torino, Via Carlo Alberto 10, 10123, Turin, Italy
2. Dipartimento di Matematica, Universit?? degli Studi di Bari, Via Orabona 4, 70125, Bari, Italy
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| Abstract: | We study the sum of weighted Lebesgue spaces, by considering an abstract measure space (W,A,m){(\Omega ,\mathcal{A},\mu)} and investigating the main properties of both the Banach space
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L( W) = {u1+u2:u1 ? Lq1 (W),u2 ? Lq2 ( W) }, Lqi ( W) :=Lqi ( W,dm),L\left( \Omega \right) =\left\{u_{1}+u_{2}:u_{1} \in L^{q_{1}} \left(\Omega \right),u_{2} \in L^{q_{2}} \left( \Omega \right) \right\}, L^{q_{i}} \left( \Omega \right) :=L^{q_{i}} \left( \Omega ,d\mu \right), |
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