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\(L^ p\) bounds on singular integrals in homogenization. (English) Zbl 0761.42008

The authors study the \(L^ p\)-boundedness of operators \[ (\partial/\partial x^ \alpha)(\partial/\partial x^ \beta)(-L)^{- 1},\;(\partial/\partial x^ \alpha)(-L)^{-1/2},\;(-L)^{- 1/2}(\partial/\partial x^ \alpha),\;(\partial/\partial x^ \alpha)(- L)^{-1}(\partial/\partial x^ \beta), \] \(1\leq\alpha,\beta\leq n\), where \(L\) belongs to a class of the second-order elliptic operators arising in the theory of homogenization.

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
35J99 Elliptic equations and elliptic systems
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