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Some Weighted Norm Estimates for the Composition of the Homotopy and Green’s Operator

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  • Huacan Li
  • Qunfang Li

Abstract

We establish the Ar(D)‐weighted integral inequality for the composition of the Homotopy T and Green’s operator G on a bounded convex domain and also motivated it to the global domain by the Whitney cover. At the same time, we also obtain some (p, q)‐type norm inequalities. Finally, as applications of above results, we obtain the upper bound for the Lp norms of T(G(u)) or (T(G(u))) B in terms of Lq norms of u or du.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:941658
DOI: 10.1155/2014/941658
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