## $$L^ p$$ 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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### References:

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